Past String Theory Seminar

In the absence of background fluxes and sources, the compactification of string theories on Calabi-Yau threefolds leads to supersymmetric solutions.Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the geometry to break the Calabi-Yau conditions, and to satisfy, instead, the weaker condition of reduced structure. In this talk I will discuss manifolds with SU(3) structure, and their relevance for heterotic string compacitications. I will focus on domain wall solutions and how explicit example geometries can be constructed.

Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle

compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding

self-dual strings, respectively. We study an index which counts BPS

instantons with electric charges in Coulomb and symmetric phases. We first

prove the existence of unique threshold bound state of U(1) instantons for

any instanton number. By studying SU(N) self-dual strings in the Coulomb

phase, we find novel momentum-carrying degrees on the worldsheet. The total

number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory.

We finally propose that our index can be used to study the symmetric phase of

this theory, and provide an interpretation as the superconformal index of the

sigma model on instanton moduli space. 

String theory on a torus requires the introduction of dual coordinates

conjugate to string winding number. This leads to physics and novel geometry in a doubled space. This will be

compared to generalized geometry, which doubles the tangent space but not the manifold.

For a d-torus,   string theory can be formulated in terms of an infinite

tower of fields depending on both the d torus coordinates and the d dual

coordinates. This talk focuses on a finite subsector  consisting of a metric

and B-field (both d x d matrices) and a dilaton all depending on the 2d

doubled torus coordinates.

The double field theory is constructed and found to have a novel symmetry

that reduces to diffeomorphisms and anti-symmetric tensor gauge

transformations in certain circumstances. It also has manifest T-duality

symmetry which provides a generalisation of the usual Buscher rules to

backgrounds without isometries. The theory has a real dependence on the full

doubled geometry:  the dual dimensions are not auxiliary. It is concluded

that the doubled geometry is physical and dynamical.

We establish a correspondence between generalized quiver gauge theories in

four dimensions and congruence subgroups of the modular group, hinging upon

the trivalent graphs which arise in both. The gauge theories and the graphs

are enumerated and their numbers are compared. The correspondence is

particularly striking for genus zero torsion-free congruence subgroups as

exemplified by those which arise in Moonshine. We analyze in detail the

case of index 24, where modular elliptic K3 surfaces emerge: here, the

elliptic j-invariants can be recast as dessins d'enfant which dictate the

Seiberg-Witten curves.

In this talk, I will focus on an infinite class of 3d N=4 gauge theories

which can be constructed from a certain set of ordered pairs of integer

partitions. These theories can be elegantly realised on brane intervals in

string theory.  I will give an elementary review on such brane constructions

and introduce to the audience a symmetry, known as mirror symmetry, which

exchanges two different phases (namely the Higgs and Coulomb phases) of such

theories.  Using mirror symmetry as a tool, I will discuss a certain

geometrical aspect of the vacuum moduli spaces of such theories in the

Coulomb phase. It turns out that there are certain infinite subclasses of

such spaces which are special and rather simple to study; they are complete intersections. I will mention some details and many interesting features of these spaces.

A simple formula is given for the $n$-field tree-level MHV gravitational

amplitude, based on soft limit factors. It expresses the full $S_n$ symmetry

naturally, as a determinant of elements of a symmetric ($n \times n$) matrix.

I will discuss some recent progress connecting different quiver gauge theories and some applications of these results.

The partition function of 3d N=2 superconformal theories on the

3-sphere can be computed exactly by localization methods. I will explain

some sublteties associated to that important result. As a by-product, this

analysis establishes the so-called F-maximization principle for N=2 SCFTs in

3d: the exact superconformal R-charge maximizes the 3-sphere free energy

F=-log Z.

The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field

theories. Over the past few years there has been a surge of activity aimed at finding

possible applications to condensed matter systems. One focus has been to holographically

realise various kinds of phases via the construction of fascinating new classes of black

hole solutions. In this framework, I will discuss the possibility of describing finite

temperature phase transitions leading to spontaneous breaking of translational invariance of

the dual field theory at strong coupling. Along with the general setup I will also discuss

specific string/M theory embeddings of the corresponding symmetry breaking modes leading to

the description of such phases.

In this talk we will review M-theory dualities and recent attempts to make these dualities manifest in eleven-dimensional supergravity. We will review the work of Berman and Perry and then outline a prescription, called non-linear realisation, for making larger duality symmetries manifest. Finally, we will explain how the local symmetries are described by generalised geometry, which leads to a duality-covariant constraint that allows one to reduce from generalised space to physical space.

The moduli space of supersymmetric (eighth-BPS) giant gravitons in $AdS_5 \times S^5$ is a limit of projective spaces. Quantizing this moduli space produces a Fock space of oscillator states, with a cutoff $N$ related to the rank of the dual $U(N)$ gauge group. Fuzzy geometry provides the ideal set of techniques for associating points or regions of moduli space to specific oscillator states. It leads to predictions for the spectrum of BPS excitations of specific worldvolume geometries. It also leads to a group theoretic basis for these states, containing Young diagram labels for $U(N)$ as well as the global $U(3)$ symmetry group. The problem of constructing gauge theory operators corresponding to the oscillator states and  some recent progress in this direction are explained.

I will describe the recent construction of new supersymmetric compactifications of the heterotic string which yield just the spectrum of the MSSM at low energies. The starting point is the standard embedding solution on a Calabi-Yau manifold with Euler number -6 with various choices of Wilson lines, i.e., various choices of discrete holonomy for the gauge bundle. Although they yield three net generations of standard model matter, such models necessarily have a larger gauge group than the standard model, as well as exotic matter content. Families of stable bundles can be obtained by deformation of these simple solutions, the deformation playing the dual role of partially breaking the gauge group and reducing the matter content, and in this way we construct more realistic models. The moduli space breaks up into various branches depending on the initial choice of Wilson lines, and on eight of these branches we find models with exactly the standard model gauge group, three generations of quarks and leptons, two Higgs doublets, and no other massless charged states. I will also comment on why these are possibly the unique models of this type.

We study pure Seiberg-Witten theories with $SU(r+1)$ and $Sp(2r)$ gauge groups with no flavors. We study singularity loci of moduli space of the Seiberg-Witten curve. Using exterior derivative and discriminant operators, we can find Argyres-Douglas loci of the SW theory. We also compute BPS charges of the massless dyons of $SU$ and $Sp$ SW theory. In a detailed example of $C_2=Sp(4)$, we find 6 points in the moduli space where we have 2 massless BPS dyons, and 3 of them give Argyres-Douglas loci. We show that BPS charges of the massless dyons jump as we go across Argyres-Douglas loci, giving an explicit example of Argyres-Douglas loci living inside the wall of marginal stability. (Based on work in progress with Keshav Dasgupta)

I shall describe the construction of the four-brane giant graviton on $\mathrm{AdS}_4\times \mathbb{CP}^3$ (extended and moving in the complex projective space), which is dual to a subdeterminant operator in the ABJM model. This dynamically stable, BPS configuration factorizes at maximum size into two topologically stable four-branes (each wrapped on a different $\mathbb{CP}^2 \subset \mathbb{CP}^3$ cycle) dual to ABJM dibaryons. Our study of the spectrum of small fluctuations around this four-brane giant provides good evidence for a dependence in the spectrum on the size, $\alpha_0$, which is a direct result of the changing shape of the giant’s worldvolume as it grows in size. I shall finally comment upon the implications for operators in the non-BPS, holomorphic sector of the ABJM model.

I will present a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. These loops are calculated on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. I will comment about the feasibility of deriving all-loop results for these Wilson loops.

I will discuss the dynamical emergence of IR conformal invariance describing the low energy excitations of near-extremal R-charged global AdS${}_5$ black holes. To keep some non-trivial dynamics in the sector of ${\cal N}=4$ SYM captured by the near horizon limits describing these IR physics, we are lead to study large N limits in the UV theory involving near vanishing horizon black holes. I will consider both near-BPS and non-BPS regimes, emphasising the differences in the local AdS${}_3$ throats emerging in both cases. I will compare these results with the predictions obtained by Kerr/CFT, obtaining a natural quantisation for the central charge of the near-BPS emergent IR CFT describing the open strings stretched between giant gravitons.

In just the last year it has been realized that one can define supersymmetric gauge theories on non-trivial compact curved manifolds, coupled to a background R-symmetry gauge field, and moreover that expectation values of certain BPS operators reduce to finite matrix integrals via a form of localization. I will argue that a general approach to this topic is provided by the gauge/gravity correspondence. In particular, I will present several examples of supersymmetric gauge theories on different 1-parameter deformations of the three-sphere, which have a large N limit, together with their gravity duals (which are solutions to Einstein-Maxwell theory). The Euclidean gravitational partition function precisely matches a large N matrix model evaluation of the field theory partition function, as an exact \emph{function} of the deformation parameter.

I will study the sequestering of blow-up fields through a CFT in a toroidal orbifold setting. In particular, I will examine the disk correlator between orbifold blow-up moduli and matter Yukawa couplings. Blow-up moduli appear as twist fields on the worldsheet which introduce a monodromy

condition for the coordinate field X. Thus I will focus on how the presence of twist field affects

the CFT calculation of disk correlators. Further, I will explain how the results are relevant to

suppressing soft terms to scales parametrically below the gravitino mass. Last, I want to explore the

relevance of our calculation for the case of smooth Calabi-Yaus.

Consistent truncations have proved to be powerful tools in the construction of new string theory solutions. Recently, they have been employed in the holographic description of condensed matter systems. In the talk, I will present a rich class of supersymmetric consistent truncations of higher-dimensional supergravity which are based on geometric structures, focusing on the tri-Sasakian case. Then I will discuss some applications, including a general result relating AdS backgrounds to solutions with non-relativistic Lifshitz symmetry.

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.