Past String Theory Seminar

 I will present a scenario where the early universe is in a topological phase of gravity.  I will discuss a number of analogies which motivate considering gravity in such a phase. Cosmological puzzles such as the horizon problem provide a phenomenological connection to this phase and can be explained in terms of its topological nature. To obtain phenomenological estimates, a concrete realization of this scenario using Witten's four dimensional topological gravity will be used. In this model, the CMB power spectrum can be estimated by certain conformal anomaly coefficients. A qualitative prediction of this phase is the absence of tensor modes in cosmological fluctuations.

One of the lasting puzzles in quantum gravity is whether the holographic description of a gravitational system is a single quantum mechanical theory or the disorder average of many. In the latter case, multiple copies of boundary observables do not factorize into a product, but rather have higher moments. These correlations are interpreted in the bulk as due to geometries involving spacetime wormholes which connect disjoint boundaries. 

I will talk about the question of factorization and the role of wormholes for supersymmetric observables, specifically the supersymmetric index. Working with the Euclidean gravitational path integral, I will start with a bulk prescription for computing the supersymmetric index, which agrees with the usual boundary definition. Concretely, I will focus on the setting of charged black holes in asymptotically flat four-dimensional N=2 ungauged supergravity. In this case, the gravitational index path integral has an infinite family of Kerr-Newman classical saddles with different angular velocities. However, fermionic zero-mode fluctuations annihilate the contribution of each saddle except for a single BPS one which yields the expected value of the index. I will then turn to non-perturbative corrections involving spacetime wormholes, and show that fermionic zero modes are present for all such geometries, making their contributions vanish. This mechanism works for both single- and multi-boundary path integrals. In particular, only disconnected geometries without wormholes contribute to the index path integral, and the factorization puzzle that plagues the black hole partition function is resolved for the supersymmetric index. I will also present all other single-centered geometries that yield non-perturbative contributions to the gravitational index of each boundary. Finally, I will discuss implications and expectations for factorization and the status of supersymmetric ensembles in AdS/CFT in further generality. Talk based on [2107.09062] with Luca Iliesiu and Joaquin Turiaci.

The global symmetries of a d-dimensional quantum field theory (QFT), and their ’t Hooft anomalies, are conveniently captured by a topological field theory (TFT) in (d+1) dimensions, which we may refer to as the Symmetry TFT of the given d-dimensional QFT. This point of view has a vast range of applicability: it encompasses both ordinary symmetries, as well as generalized symmetries. In this talk, I will discuss systematic methods to compute the Symmetry TFT for QFTs realized by M-theory on a singular, non-compact space X. The desired Symmetry TFT is extracted from the topological couplings of 11d supergravity, via reduction on the space L, the boundary of X. The formalism of differential cohomology allows us to include discrete symmetries originating from torsion in the cohomology of L. I will illustrate this framework in two classes of examples: M-theory on an ALE space (engineering 7d SYM theory); M-theory on Calabi-Yau cones (engineering 5d superconformal field theories).

The analytic structure of scattering amplitudes exhibit striking
properties that are not at all evident from the first principles of
Quantum Field Theory. These are often rich and powerful enough to be
considered as their defining features, and this makes the problem of
finding a set of universal rules a compelling one. I will review the
recently mounting evidence for the relevance of tropical Grassmannians
in this respect, including implications on symbol alphabets and
adjacency conditions

 I will review some well-established relationships between four manifolds and vertex algebras that can be deduced from studying the M5-brane worldvolume theory, and outline some of the corresponding results in mathematics which have been understood so far. I will then describe a proposal of Gaiotto-Rapcak to generalize these ideas to the setting of multiple M5 branes wrapping divisors in toric Calabi-Yau threefolds, and explain work in progress on understanding the mathematical implications of this proposal as a complex network of relationships between the enumerative geometry of sheaves on threefolds and the representation theory of affine Lie algebras.

It is well-known that the spectral data of the Gaudin model associated to a finite semisimple Lie algebra is encoded by the differential data of certain flat connections associated to the Langlands dual Lie algebra on the projective line with regular singularities, known as oper/Gaudin correspondence. Recently, some progress has been made in understanding the correspondence associated with affine Lie algebras. I will present a physical perspective from Kondo line defects, physically describing a local impurity chirally coupled to the bulk 2d conformal field theory. The Kondo line defects exhibit interesting integrability properties and wall-crossing behaviors, which are encoded by the generalized monodromy data of affine opers. In the physics literature, this reproduces the known ODE/IM correspondence. I will explain how the recently proposed 4d Chern Simons theory provides a new perspective which suggests the possibility of a physicists’ proof. 

 In this talk I will discuss an algorithm to piecewise dualise linear quivers into their mirror duals. This applies to the 3d N=4 version of mirror symmetry as well as its recently introduced 4d counterpart, which I will review. The algorithm uses two basic duality moves, which mimic the local S-duality of the 5-branes in the brane set-up of the 3d theories, and the properties of the S-wall. The S-wall is known to correspond to the N=4 T[SU(N)] theory in 3d and I will argue that its 4d avatar corresponds to an N=1 theory called E[USp(2N)], which flows to T[SU(N)] in a suitable 3d limit. All the basic duality moves and S-wall properties needed in the algorithm are derived in terms of some more fundamental Seiberg-like duality, which is the Intriligator--Pouliot duality in 4d and the Aharony duality in 3d.

We will review how one can find families of 4d N=1 SCFTs starting from known 6d (1,0) SCFTs. 

Then we will discuss a relation between 6d RG-flows and 4d RG-flows, where the 4d RG-flow relates 4d N=1 models constructed from compactification of 6d (1,0) SCFTs related by the 6d RG-flow. We will show how we can utilize such a relation to find many "Lagrangians" for strongly coupled 4d models. Relating 6d SCFTs to 4d models as mentioned above will result in geometric reasoning behind some 4d phenomena such as dualities and symmetry enhancement.

Such a program generates a large database of known 4d N=1 SCFTs with many interrelations one can use in future efforts to construct 4d N=1 SCFTs from string theory directly.

We discuss the Mellin amplitude formalism for Conformal Field Theories
(CFT's).  We state the main properties of nonperturbative CFT Mellin
amplitudes: analyticity, unitarity, Polyakov conditions and polynomial
boundedness at infinity. We use Mellin space dispersion relations to
derive a family of sum rules for CFT's. These sum rules suppress the
contribution of double twist operators. We apply the Mellin sum rules
to: the epsilon-expansion and holographic CFT's.

Scattering amplitudes in N=4 super-Yang-Mills theory are known to be functions of cluster variables of Gr(4,n) and certain algebraic functions of cluster variables. In this talk we give an overview of the known cluster algebraic structure of both tree amplitudes and the symbol of loop amplitudes. We suggest an algorithm for computing symbol alphabets by solving matrix equations of the form C.Z = 0 associated with plabic graphs. These matrix equations associate functions on Gr(m,n) to parameterizations of certain cells of Gr_+ (k,n) indexed by plabic graphs. We are able to reproduce all known algebraic functions of cluster variables appearing in known symbol alphabets. We further show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving C.Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of Gr_+ (n-4,n). Finally we discuss a property of the symbol called cluster adjacency.

A proposal for the worldsheet string theory that is dual to free N=4 SYM in 4d will be explained. It is described by a free field sigma model on the twistor space of AdS5 x S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 x S3. I will explain how our proposal fits into the general framework of AdS/CFT, and review the various checks that have been performed.
 

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. I will also discuss how this correspondence is modified in more general contexts, including e.g. Chern-Simons terms. 

I will discuss a precise connection between renormalization group (RG) and quantum chaos. Every RG flow between two conformal fixed points can be described in terms of the dynamics of Nambu-Goldstone bosons of broken symmetries. The theory of Nambu-Goldstone bosons can be viewed as a theory in anti-de Sitter space with the flat space limit. This enables an equivalent formulation of these 4d RG flows in terms of spectral deformations of a generalized free CFT in 3d. This approach provides a precise relation between C-functions associated with 4d RG flows and certain out-of-time-order correlators that diagnose chaos in 3d. As an application, I will show that the 3d chaos bound imposes constraints on the low energy effective action associated with unitary RG flows in 4d with a broken continuous global symmetry in the UV. These bounds, among other things, imply that the proof of the 4d a-theorem remains valid even when additional global symmetries are broken.

Manifolds with G2 structure allow almost contact structures. In this talk I will discuss various aspects of such structures, and their effect on certain supersymmetric configurations in string and M-theory.

This is based on recent work with Xenia de la Ossa and Matthew Magill.

We discuss constraints from perturbative unitarity and crossing on the leading contributions of the higher-dimension operators to the four-graviton amplitude in four spacetime dimensions. We focus on the leading order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest IR finite. To test the constraints we obtain nontrivial effective field theory data by computing and taking the large mass expansion of the one-loop minimally-coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, the leading EFT corrections to Einstein gravity of physical theories, both string theory and QFT coupled to gravity, end up in minuscule islands which are much smaller than what is suggested by the generic bounds obtained from consistency of the 2-2 graviton scattering amplitude. We discuss the underlying mechanism for this phenomenon.

The periods of a Calabi-Yau manifold are of interest both to number theorists and to physicists. To a number theorist the primary object of interest is the zeta function. I will explain what this is, and why this is of interest also to physicists. For applications it is important to be able to calculate the local zeta function for many primes p. I will set out a method, adapted from a procedure proposed by Alan Lauder that makes the computation of the zeta function practical, in this sense, and comment on the form of the results. This talk is based largely on the recent paper hepth 2104.07816 and presents joint work with Xenia de la Ossa and Duco van Straten.

Recent developments on the black hole information paradox have shown that Euclidean wormholes — so called “replica wormholes’’  — can dominate the von Neumann entropy as computed by a gravitational path integral, and that inclusion of these wormholes results in a unitary Page curve. This development raises some puzzles from the perspective of factorization, and has raised questions regarding what the gravitational path integral is computing. In this talk, I will focus on understanding the relationship between the gravitational path integral and the partition function via the gravitational free energy (more generally the generating functional). A proper computation of the free energy requires a replica trick distinct from the usual one used to compute the entropy. I will show that in JT gravity there is a regime where the free energy computed without replica wormholes is pathological. Interestingly, the inclusion of replica wormholes is not quite sufficient to resolve the pathology: an alternative analytic continuation is required. I will discuss the implications of this for various interpretations of the gravitational path integral (e.g. as computing an ensemble average) and also mention some parallels with spin glasses. 

Chiral fermion anomalies in any spacetime dimension are computed by evaluating an eta-invariant on a closed manifold in one higher dimension. The APS index theorem then implies that both local and global gauge anomalies are detected by bordism invariants, each being classified by certain abelian groups that I will identify. Mathematically, these groups are connected via a short exact sequence that splits non-canonically. This enables one to relate global anomalies in one gauge theory to local anomalies in another, by which we revive (from the bordism perspective) an old idea of Elitzur and Nair for deriving global anomalies. As an example, I will show how the SU(2) anomaly in 4d can be derived from a local anomaly by embedding SU(2) in U(2).

We will discuss confinement in 4d N=1 theories obtained after soft supersymmetry breaking deformations of 4d N=2 Class S theories. Confinement is characterised by a subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. The 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in N=1 SYM theories, and the theories studied by Cachazo, Douglas, Seiberg and Witten. We will also recover the dependence of confinement on the choice of gauge group and discrete theta parameters in these theories.

NOTE: unusual time! 

We discuss a class of 5-dimensional supersymmetric non-Lorentzian Lagrangians with an SU(1,3) conformal symmetry. These theories arise from reduction of 6-dimensional CFT's on a comformally compactified spacetime. We use the SU(1,3) Ward identities to find the form of the correlation functions which have a rich structure. Furthermore we show how these can be used to reconstruct  6-dimensional  CFT correlators. 
 

In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The classical bulk reconstruction is provided by the sl(2)-orbit theorem, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us to prove that the number of self-dual flux vacua is finite. I will point out how the finiteness result for supersymmetric fluxes relates to the Hodge conjecture.

 We generalize the recent holographic correspondence between an ensemble average of free bosons in two dimensions, and a Chern-Simons-like theory of gravity in three dimensions, by Afkhami-Jeddi et al and Maloney and Witten. We find that the correspondence also works for toroidal orbifolds, but we run into difficulties generalizing to K3 and Calabi-Yau sigma models. For the case of toroidal orbifolds, we extend the holographic correspondence to averages of correlation functions of twist operators by using properties of rational tangles in three-dimensional balls and their covering spaces. Based on work to appear with C. Keller, H. Ooguri, and I. Zadeh. 

I will discuss various operator algebras in supersymmetric quantum field theories in various dimensions. The operator algebras are induced and classified by generalised topological twists. Omega deformation plays an important role in connecting different sectors. This talk is based on previous works and a work in progress with Junya Yagi.

In this talk I will present an optical theorem for perturbative CFTs, which directly computes the double discontinuity of CFT correlators in terms of the discontinuities of correlators at lower loops or lower points, in analogy to the optical theoreom for scattering amplitudes. I will then discuss the application of this theorem to high-energy scattering of type IIb strings in AdS at one loop and finite 't Hooft coupling. Tidal excitations are taken into account and shown to be efficiently described by an AdS vertex function. The result is related to the 1987 flat space result of Amati, Ciafaloni and Veneziano via the flat space limit in impact parameter space.

We will discuss recent progress in understanding (ordinary and generalized) symmetries, dualities and classification of superconformal field theories in 5d and 6d, which involves the study of M-theory and F-theory compactified on Calabi-Yau threefolds.

In view of the recent observations of gravitational-wave signals from black-hole mergers, classical black-hole scattering has received considerable interest due to its relation to the classical bound-state problem of two black holes inspiraling onto each other. In this talk I will discuss the link between classical scattering of spinning black holes and quantum scattering amplitudes for massive spin-s particles. Considering the first post-Minkowskian (PM) order, I will explain how the spin-exponentiated structure of the relevant tree-level amplitude follows from minimal coupling to Einstein's gravity and in the s → ∞ limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function will be shown to encode in a simple way the classical net changes in the black-hole momenta and spins at 1PM order and to all orders in spins. I will then comment on the results and challenges at 2PM order and beyond.
 

All five-dimensional non-abelian gauge theories have a U(1)U(1)I​U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries of  the theory, namely the one-form center symmetry or ordinary flavor symmetry for theories with fundamental matter. I will explore some general dynamical properties of the candidate phases implied by the anomaly, and apply our results to supersymmetric gauge theories in five dimensions, analysing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

A vast class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a Riemann surface. These SCFTs can exhibit a variety of global symmetries, continuous or discrete, including both ordinary (0-form) symmetries, as well as generalized (higher-form) symmetries. In this talk, I will focus on discrete and higher-form symmetries in setups with M5-branes on a smooth Riemann surface. Adopting a holographic point of view, a crucial role is played by topological mass terms in 5d supergravity (similar to BF terms in four dimensions). I will discuss how the global symmetries of the boundary 4d theory are inferred from the 5d topological terms, and how one can compute 4d ‘t Hooft anomalies involving discrete and/or higher-form symmetries.

 I will review what is known and not known about the joint moments of the characteristic polynomials of random unitary matrices and their derivatives. I will then explain some recent results which relate the joint moments to an interesting class of measures, known as Hua-Pickrell measures. This leads to the proof of a conjecture, due to Chris Hughes in 2000, concerning the asymptotics of the joint moments, as well as establishing a connection between the measures in question and one of the Painlevé equations.

I will discuss an analogue of the CHY formalism in AdS. Considering the biadjoint scalar theory on AdS, I will explain how to rewrite all the tree-level amplitudes as an integral over the moduli space of punctured Riemann spheres. Contrary to the flat space, the scattering equations are operator-valued. The resulting formula is motivated via a bosonic ambitwistor string on AdS and can be proven to be equivalent to the corresponding Witten diagram computation by applying a series of contour deformations.

We will show that minimally supersymmetric SU(N+2) SQCD models in the middle of the conformal window can be engineered by compactifying certain 6d SCFTs on three punctured spheres. The geometric construction of the 4d theories predicts numerous interesting strong coupling effects, such as IR symmetry enhancements and duality. We will discuss this interplay between simple geometric and group theoretic considerations and complicated field theoretic strong coupling phenomena. For example, one of the dualities arising geometrically from different pair-of-pants decompositions of a four punctured sphere  is an $SU(N+2)$ generalization of the Intriligator-Pouliot duality of $SU(2)$ SQCD with $N_f=4$, which is a degenerate, $N=0$, instance of our discussion. 

I will talk about a novel idea on the Swampland program that uses consistency of what lives on the string probes in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the supergravity theories based on unitarity of the worldsheet CFT. I will show some of the theories with 8 or 16 supersymmetries, which are otherwise consistent looking, belong to the Swampland.

I will revisit the question of what is the holographic dual of N=6 supersymmetric Chern-Simons theories.

We discuss hyperkahler implosion spaces, their relevance to group actions and why they should fit into the symplectic duality picture. For certain groups we present candidates for the symplectic duals of the associated implosion spaces and provide computational evidence. This is joint work with Amihay Hanany and Frances Kirwan.
 

Over the last few years, it has become clear that working in sectors of large global charge leads to significant simplifications when studying strongly coupled CFTs. It allows us in particular to calculate the CFT data as an expansion in inverse powers of the large charge.
In this talk, I will introduce the large-charge expansion via the simple example of the O(2) model and will then apply it to a number of other systems which display a richer structure, such as non-Abelian global symmetry groups.
 

Vafa-Witten theory is a topologically twisted version of 4d N=4 super Yang-Mills theory. In my talk I will tell how to derive a holomorphic anomaly equation for its partition function on a Kaehler 4-manifold with b_2^+=1 and b_1=0 from the path integral of the effective theory on the Coulomb branch. I will also briefly mention an alternative and somewhat similar computation of the same holomorphic anomaly in the effective 2d theory obtained by compactification of the corresponding 6d (2,0) theory on the 4-manifold.
 

We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/diffenretial geometry, and then to computational geometry, and now to data science and AI.
With the concrete playground of the Calabi-Yau landscape, accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades, we show how the latest techniques in machine-learning can help explore problems of physical and mathematical interest.
 

In this talk, we will discuss two-dimensional theories with discrete

one-form symmetries, examples (which we have been studying

since 2005), their properties, and gauging of the one-form symmetry.

Their most important property is that such theories decompose into a

disjoint union of theories, recently deemed `universes.'

This decomposition has the effect of restricting allowed nonperturbative

sectors, in a fashion one might deem a `multiverse interference effect,'

which has had applications in topics including Gromov-Witten theory and

gauged linear sigma model phases.  After reviewing one-form symmetries

and decomposition in general, we will discuss a particular 

example in detail to explicitly illustrate these properties and 

to demonstrate how

gauging the one-form symmetry projects onto summands in the

decomposition.  If time permits, we will briefly review

analogous phenomena in four-dimensional theories with three-form symmetries,

as recently studied by Tanizaki and Unsal.

In this talk, I will argue how the observation that four-dimensional N=2 superconformal field theories are interconnected via the operation of Higgsing can be turned into an effective method to construct such SCFTs. A fundamental role is played by the (generalized) free field realization of the associated VOAs.

I will discuss recently published examples of SCFTs in
two dimensions and their dual backgrounds. Aspects of the
integrability of these string backgrounds will be described in
correspondence with those of the dual SCFTs. The comparison with four and
six dimensional examples will be presented. It time allows, the case of
conformal quantum mechanics will also be addressed.

String sigma-models relevant in the AdS/CFT correspondence are highly non-trivial two-dimensional field theories for which predictions at finite coupling exist, assuming integrability and/or the duality itself.  I will discuss general features of the perturbative approach to these models, and present progress on how to go extract finite coupling information in the most possibly general way, namely via the use of lattice field theory techniques. I will also present new results on certain ``defect-CFT’' correlators  at strong coupling. 

I will describe work exploring the spectrum of two-dimensional unitary conformal field theories(CFT) with no extended chiral algebra and central charge larger than one. I will revisit a classical result from analytic number theory by Rademacher, which provides an exact formula for the Fourier coefficients of modular forms of non-positive weight. Generalizing this, I will explain how we employed Rademacher's idea to study the spectral density of two-dimensional CFT of our interest. The expression is given in terms of a Rademacher expansion, which converges for nonzero spin. The implications of our spectral density to the pure gravity in AdS3 will be discussed.

We discuss properties of the cosmological horizon of a de Sitter universe, and compare to those of ordinary black holes. We consider both the Lorentzian and Euclidean picture. We discuss the relation to the sphere partition function and give a group-theoretic picture in terms of the de Sitter group. Time permitting we discuss some properties of three-dimensional de Sitter theories with higher spin particles. 

I will discuss the origin of the choice of global structure
--- or equivalently, the choice for which higher p-form symmetries are
present in the theory --- for various (Lagrangian and non-Lagrangian)
field theories in terms of their realization in IIB and M-theory. I
will explain how this choice on the field theory side can be traced
back to the fact that fluxes in string/M-theory do not commute in the
presence of torsion. I will illustrate how these ideas provide a
stringy explanation for the fact that six-dimensional (2,0) and (1,0)
theories generically have a partition vector (as opposed to a partition
function) and explain how this reproduces the classification of N=4
theories provided by Aharony, Seiberg and Tachikawa. Time permitting, I
will also explain how to use these ideas to obtain the algebra of
higher p-form symmetries for 5d SCFTs arising from M-theory at
arbitrary isolated toric singularities, and to classify global forms
for various 4d theories in the presence of duality defects.

In the process of studying the zeta-function for one parameter families of Calabi-Yau manifolds we have been led to a manifold, for which the quartic numerator of the zeta-function factorises into two quadrics remarkably often. Among these factorisations, we find persistent factorisations; these are determined by a parameter that satisfies an algebraic equation with coefficients in Q, so independent of any particular prime.  We note that these factorisations are due a splitting of Hodge structure and that these special values of the parameter are rank two attractor points in the sense of IIB supergravity. To our knowledge, these points provide the first explicit examples of non-singular, non-rigid rank two attractor points for Calabi-Yau manifolds of full SU(3) holonomy. Modular groups and modular forms arise in relation to these attractor points in a way that, to a physicist, is unexpected. This is a report on joint work with Xenia de la Ossa, Mohamed Elmi and Duco van Straten.