Past String Theory Seminar

It is well known to mathematicians that there is a deep relationship between the arithmetic of algebraic varieties and their geometry.  

In recent years, there has been increasing evidence for a geometric representation of quantum chaos within Einstein's theory of general relativity. Despite the lack of a complete theoretical framework, this overview will explore various examples of this phenomenon. It will also discuss the lessons we have learned from it to address several existing puzzles in quantum gravity, such as the black hole information paradox and off-shell wormhole geometries.

Entanglement entropy has long served as a key diagnostic of topological order in (2+1) dimensions. In particular, the topological entanglement entropy captures a universal quantity (the total quantum dimension) of the underlying topological order. However, this information alone does not uniquely determine which topological order is realized, indicating the need for more refined probes. In this talk, I will present a family of quantities formulated as multi-entropy measures, including examples such as reflected entropy and the modular commutator. Unlike the conventional bipartite setting of topological entanglement entropy, these multi-entropy measures are defined for tripartite partitions of the Hilbert space and capture genuinely multipartite entanglement. I will discuss how these measures encode additional universal data characterizing topologically ordered ground states.

Symmetry Topological Field Theories (SymTFTs) are topological field theories that encode the symmetry structure of global symmetries in terms of a theory in one higher dimension. While SymTFTs for internal (global) symmetries have been highly successful in characterizing symmetry aspects in the last few years, a corresponding framework for spacetime symmetries remains unexplored. We propose an extension of the SymTFT framework to include spacetime symmetries. In particular, we propose a SymTFT for the conformal symmetry in various spacetime dimensions. We demonstrate that certain BF-type theories, closely related to topological gravity theories, possess the correct topological operator content and boundary conditions to realize the conformal algebra of conformal field theories living on boundaries. As an application, we show how effective theories with spontaneously broken conformal symmetry can be derived from the SymTFT, and we elucidate how conformal anomalies can be reproduced in the presence of even-dimensional boundaries.
 

For homogeneous, defect-free TQFTs, (1) n+\epsilon-dimensional versions of the theories are relatively easy to construct; (2) an n+\epsilon-dimensional theory can be extended to n+1-dimensional (i.e. the top-dimensional path integral can be defined) if certain more restrictive conditions related to handle cancellation are satisfied; and (3) applying this path integral construction to a handle decomposition of an n+1-manifold yields a state sum description of the path integral.  In this talk, I'll show that the same pattern holds for defect TQFTs.  The adaptation of homogeneous results to the defect setting is mostly straightforward, with the only slight difficulty being the purely topological problem of generalizing handle theory to manifolds with defects.  If time allows, I'll describe two applications: a Verlinde-like dimension formula for the dimension of the ground state of fracton systems, and a generalization, to arbitrary dimension, of Ostrik's theorem relating algebra objects to modules (gapped boundaries).

Einstein’s equations are difficult to solve and if you want to compute something in holography knowing an explicit metric seems to be essential. Or is it? For some theories, observables, such as on-shell actions and free energies, are determined solely in terms of topological data, and an explicit metric is not needed. One of the key tools that has recently been used for this programme is equivariant localization, which gives a method of computing integrals on spaces with a symmetry. In this talk I will give a pedestrian introduction to equivariant localization before showing how it can be used to compute the on-shell action of 6d Romans Gauged supergravity. 
 

I will describe a new method for constructing conformal blocks for the Virasoro vertex algebra with central charge c=1, by "nonabelianization", relating them to conformal blocks for the Heisenberg algebra on a branched double cover. The construction is joint work with Qianyu Hao. Special cases give rise to formulas for tau-functions and solutions of integrable systems of PDE, such as Painleve I and its higher analogues. The talk will be reasonably self-contained (in particular I will explain what a conformal block is).

We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature--it therefore constitutes a quantum topological order at finite temperature. The model of interest is known as the fermionic toric code, a variant of the usual 3D toric code, which admits emergent fermionic point-like excitations. The fermionic toric code, importantly, possesses an anomalous 2-form symmetry, associated with the space-like Wilson loops of the fermionic excitations. We argue that it is this symmetry that imbues low-temperature thermal states with a novel topological order and long-range entanglement. Based on the current classification of three-dimensional topological orders, we expect that the low-temperature thermal states of the fermionic toric code belong to an equilibrium phase of matter that only exists at nonzero temperatures. We conjecture that further examples of topological orders at nonzero temperatures are given by discrete gauge theories with anomalous 2-form symmetries. Our work therefore opens the door to studying quantum topological order at nonzero temperature in physically realistic dimensions.

Dirac’s quantum theory of magnetic monopoles requires a Dirac string attached to each monopole, and it is important that the field equations do not depend on the positions of the Dirac strings, provided that they comply with the Dirac veto: they must not intersect the worldliness of electrically charged particles. This theory is revisited, and it is shown that it has generalised symmetries related to the freedom of moving the Dirac strings. The Dirac veto is interpreted as an anomaly and the possibility of cancelling the anomaly by embedding in a higher-dimensional theory will be discussed. 

This talk is based on arXiv:2411.18741.

We consider quantum electrodynamics in 2+1 dimensions (QED3) with N matter fields and Chern-Simons level k. For small values of k and N, this theory describes various experimentally relevant systems in condensed matter, and is also conjectured to be part of a web of non-supersymmetric dualities. We compute the scaling dimensions of monopole operators in a large N and k expansion, which appears to be extremely accurate even down to the smallest values of N and k, and allows us to find dynamical evidence for these dualities and make predictions about the phase transitions. For instance, we combine these estimates with the conformal bootstrap to predict that the notorious Neel-VBS transition (QED3 with 2 scalars) is tricritical, which was recently confirmed by independent lattice simulations. Lastly, we propose a novel phase diagram for QED3 with 2 fermions, including duality with the O(4) Wilson-Fisher fixed point.

I will outline some recent progress in identifying realistic models of particle physics in heterotic string theory, supported by several mathematical and computational advancements which include: analytic expressions for bundle valued cohomology dimensions on complex projective varieties, heuristic methods of discrete optimisation such as reinforcement learning and genetic algorithms, as well as efficient neural-network approaches for the computation of Ricci-flat metrics on Calabi-Yau manifolds, hermitian Yang-Mills connections on holomorphic vector bundles and bundle valued harmonic forms. I will present a proof of concept computation of quark masses in a string model that recovers the exact standard model spectrum and discuss several other models that can accommodate the entire range of flavour parameters observed in the standard model. 

In this talk I will review recent results on the development of a form factor program for integrable quantum field theories (IQFTs) perturbed by irrelevant operators. It has been known for a long time that under such perturbations integrability is preserved and that the two-body scattering phase gets deformed in a simple manner. The consequences of such a deformation are stark, leading to theories that exhibit a so-called Hagedorn transition and no UV completion. These phenomena manifest physically in several distinct ways. In our work we have mainly asked the question of how the deformation of the S-matrix translates into the correlation functions of the deformed theory. Does the scaling of correlators at long and short distances capture any of the "pathologies" mentioned above? Can our understanding of irrelevant perturbations tell us something about the space of IQFTs and about their form factors? In this talk I will answer these questions in the afirmative, summarising work in collaboration with Stefano Negro, Fabio Sailis and István M. Szécsényi.

I will discuss the recent progress in the numerical bootstrap of the 3d Ising CFT using the correlation functions of stress-energy tensor and the relevant scalars. This numerical bootstrap setup gives excellent results which are two orders of magnitude more accurate than the previous world's best. However, it also presents many significant technical challenges. Therefore, in addition to describing in detail the numerical results of this work, I will also explain the state-of-the art numerical bootstrap methods that made this study possible. Based on arXiv:2411.15300 and work in progress.

We’ll begin by introducing homotopy algebras (assuming no background) and their intimate connection to quantum field theory, with a briefly summary of some applications: scattering amplitude recursion relations, colour-kinematics duality, and generalised asymptotic observables. We’ll then introduce (deformed) Alexandrov–Kontsevich–Schwarz–Zaboronsky theories as the paradigmatic example of this framework, before developing their applications to gravity in two, three and four dimensions.   

Gauging is a systematic way to construct a model with non-invertible symmetry from a model with ordinary group-like symmetry. In 2+1d dimensions or higher, one can generalize the standard gauging procedure by stacking a symmetry-enriched topological order before gauging the symmetry. This generalized gauging procedure allows us to realize a large class of non-invertible symmetries. In this talk, I will describe the generalized gauging of finite group symmetries in 2+1d lattice models. This talk will be based on my ongoing work with L. Bhardwaj, S.-J. Huang, S. Schäfer-Nameki, and A. Tiwari.

When tensor products of N minimal models accumulate at central charge N, they also admit relevant operators arbitrarily close to marginality. This raises the tantalizing possibility that they can be use to reach purely Virasoro symmetric CFTs where the breaking of extended chiral symmetry can be seen in a controlled way. This talk will give an overview of the theories where this appears to be the case, according to a brute force check at low lying spins. We will also encounter an interesting non-example where the same type of analysis can be used to give a simpler proof of integrability.

"The question of whether an impurity can be screened by bulk degrees of freedom is central to the study of defects and to (variations of) the Kondo problem. In this talk I discuss how symmetry, generalized or not, can give serious constraints on the possible scenarios at long distances. These can be quantified in the UV where the defect is weakly coupled. I will give some examples of interesting symmetric defect RG flows in (1+1) and (2+1)d.

Based on https://arxiv.org/pdf/2412.18652 and work in progress."

Celestial Holography posits the existence of a holographic description of gravitational theories in asymptotically flat space-times. To date, top-down constructions of such dualities involve a combination of twisted holography and twistor theory. The gravitational theory is the closed string B model living in a suitable twistor space, while the dual is a chiral 2d gauge theory living on a stack of D1 branes wrapping a twistor line. I’ll talk about a variant of these models that yields a theory of self-dual Einstein gravity (via the Plebanski equations) in four dimensions. This is based on work in progress with Roland Bittleston, Kevin Costello & Atul Sharma.

Realizing chiral global symmetries on a finite lattice is a long-standing challenge in lattice gauge theory, with potential implications for non-perturbative regularization of the Standard Model. One of the simplest examples of such a symmetry is the axial U(1) symmetry of the 1+1d massless Dirac fermion field theory: it acts by equal and opposite phase rotations on the left- and right-moving Weyl components of the Dirac field. This field theory also has a vector U(1) symmetry which acts identically on left- and right-movers. The two U(1) symmetries exhibit a mixed anomaly, known as the chiral anomaly. In this talk, we will discuss how both symmetries are realized as ordinary U(1) symmetries of an "ultra-local" lattice Hamiltonian, on a finite-dimensional Hilbert space. Intriguingly, the anomaly of the Abelian U(1) symmetries in the infrared (IR) field theory is matched on the lattice by a non-Abelian Lie algebra. The lattice symmetry forces the low-energy phase to be gapless, closely paralleling the effects of the anomaly in the field theory.

In this talk I will explain how the size of the Einstein-Rosen (ER) bridge dual to the Double Scaled SYK (DSSYK) model saturates at late times because of finiteness of the underlying quantum Hilbert space.  I will extend recent work implying that the ER bridge size equals the spread complexity of the dual DSSYK theory with an appropriate initial state.  This work shows that the auxiliary "chord basis'' used to solve the DSSYK theory is the physical Krylov basis of the spreading quantum state.  The ER bridge saturation follows from the vanishing of the Lanczos spectrum, derived by methods from Random Matrix Theory (RMT).

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. Within this paradigm, a framework has emerged enabling a calculus of topological defects in terms of a higher-dimensional topological quantum field theory. In this seminar, I will discuss aspects of this construction for Euclidean lattice field theories. Exploiting this framework, I will present generalisations of the celebrated Kramers-Wannier duality of the Ising model, as combinations of gauging procedures and generalised Fourier transforms of the local weights encoding the dynamics. If time permits, I will discuss implications of this framework for the real-space renormalisation group flow of these theories.

: With motivation from string compactifications, I will present work on the use of machine learning methods for the computation of geometric and topological properties of Calabi-Yau manifolds.

 One of the main entries in the AdS/CFT dictionary is a relation between the bulk on-shell partition function with specified boundary conditions and the generating function of correlation functions of primary operators in the boundary CFT. In this talk, I will show how to construct a similar relation for gravity in 4d asymptotically flat spacetimes. For simplicity, we will restrict to the leading infrared sector, where a careful treatment of soft modes and their canonical partners leads to a non-vanishing on-shell action. I will show that this action localizes to a codimension-2 surface and coincides with the generating function of 2d CFT correlators involving insertions of Kac-Moody currents. The latter were previously shown, using effective field theory methods, to reproduce the leading soft graviton theorems in 4d. I will conclude with comments on the implications of these results for the computation of soft charge fluctuations in the vacuum. 

In the talk, I will start by recalling some basics of optimal transport and how it can be used to define Ricci curvature lower bounds for singular spaces, in a synthetic sense. Then, I will present some joint work with De Luca-De Ponti and Tomasiello,  where we show that some singular spaces,  naturally showing up in gravity compactifications (namely, Dp-branes),  enter the aforementioned setting of non-smooth spaces satisfying Ricci curvature lower bounds in a synthetic sense.  Time permitting, I will discuss some applications to the Kaluza-Klein spectrum.

In this talk I will discuss asymmetric orbifolds and will focus on their application to toroidal compactifications of heterotic string theory. I will consider theories in 6 and 4 dimensions with 16 supercharges and reduced rank. I will present a novel formalism, based on the Leech lattice, to construct ‘islands’ without vector multiplets.

Three-dimensional QFTs with 8 supercharges (N=4 supersymmetry) are a rich playground rife with connections to mathematics. For example, they admit two topological twists and furnish a three-dimensional analogue of the famous mirror symmetry of two-dimensional N=(2,2) QFTs, creatively called 3d mirror symmetry, that exchanges these twists. Recently, there has been increased interest in so-called rank 0 theories that typically do not admit Lagrangian descriptions with manifest N=4 supersymmetry, but their topological twists are expected to realize finite, semisimple TQFTs which are amenable to familiar descriptions in terms of, e.g., modular tensor categories and/or rational vertex operator algebras. In this talk, based off of joint work (arXiv:2406.00138) with Thomas Creutzig and Heeyeon Kim, I will introduce two families of rank 0 theories exchanged by 3d mirror symmetry and various mathematical conjectures stemming from our analysis thereof.

In this talk I will describe the systematic construction of strongly interacting RG fixed points with a finite disorder strength.  Such random-field disorder is quite common in condensed matter experiment, necessitating an understanding of the effects of this disorder on the properties of such fixed points. In the past, such disordered fixed points were accessed using e.g. epsilon expansions in perturbative quantum field theory, using the replica method to treat disorder.  I will show that holography gives an alternative picture for RG flows towards disordered fixed points.  In holography, spatially inhomogeneous disorder corresponds to inhomogeneous boundary conditions for an asymptotically-AdS spacetime, and the RG flow of the disorder strength is captured by the solution to the Einstein-matter equations. Using this construction, we have found analytically-controlled RG fixed points with a finite disorder strength.  Our construction accounts for, and explains, subtle non-perturbative geometric effects that had previously been missed.  Our predictions are consistent with conformal perturbation theory when studying disordered holographic CFTs, but the method generalizes and gives new models of disordered metallic quantum criticality.

I shall review some aspects of the relationship between scale and conformal invariance in 2-dimensional sigma models.  Then, I shall explain how such an investigation is related to the Perelman's ideas of proving the Poincare' conjecture.  Using this, I shall demonstrate that scale invariant sigma models  with B-field coupling and  compact target space  are conformally invariant. Several examples will also be presented that elucidate the results.  The talk is based on the arXiv paper 2404.19526.

One of the major insights gained from holographic duality is the relation between the physics of black holes and quantum chaotic systems. This relation is made precise in the duality between two dimensional JT gravity and random matrix theory.  In this work, we generalize this to a duality between AdS3 gravity and a random ensemble of approximate CFT's.  The latter is described by a combined tensor and matrix model, describing the OPE coefficients and spectrum of a theory that approximately satisfies the bootstrap constraints.   We show that the Feynman diagrams of the random ensemble produce a sum over 3 manifolds that agrees with the partition function of 3d gravity.  A crucial element of this dictionary is the Virasoro TQFT, which defines the bulk gravitational path integral via the cutting and sewing relations of topological field theory.  Time permitting, we will explain why this TQFT has gravitational edge modes degrees of freedom whose entanglement gives rise to gravitational entropy.

The progress in our understanding of symmetries in QFT has led to the proposal that the complete information on a symmetry structure is encoded in a TQFT in one dimension higher, known as the Symmetry TFT. This picture is well understood for finite symmetries, and I will explain the extension to continuous symmetries in the first part of the talk, based on a paper with F. Benini. This extension requires studying new TQFTs with a non-compact spectrum of operators. Like for finite symmetries, these TQFTs capture anomalies and topological manipulations via their topological boundary conditions. The main new ingredient for continuous symmetries is dynamical gauging, which is described by maps between different TQFTs. I will use this to derive the Symmetry TFT for the non-invertible chiral symmetry of QED. Moreover, the various TQFTs related by dynamical gauging arise as different boundary conditions of a unique TQFT in two dimensions higher. In the second part of the talk, based on work in progress with F. Benini and G. Rizi, I will use these tools to derive some new connections between the Symmetry TFTs and the universal EFTs describing the spontaneous symmetry breaking of any (generalized) global symmetry.

In this talk, I describe an exact duality between the double scaling limit of the SYK model and quantum geometry of de Sitter spacetime in three dimensions. The duality maps the so-called chord rules that specify the exact SYK correlations functions to the skein relations that govern the topological interactions between world-line operators in 3D de Sitter gravity.

This talk is part of the series of Willis Lamb Lectures in Theoretical Physics. Herman Verlinde is the Lamb Lecturer of 2024.

What is the bare minimum needed to get a unitarity-consistent black hole radiation entropy curve? In this talk, I will show how to capture both Hawking's non-unitary entropy curve, and density matrix-connecting contributions that restore unitarity, in a toy quantum system with chaotic dynamics. The motivation is to find the simplest possible dynamical model, dropping all superfluous details, that captures this aspect of gravitational physics. In the model, the Hamiltonian obeys random matrix statistics within microcanonical windows, the entropy of the averaged state gives the non-unitary curve, the averaged entropy gives the unitary curve, and the difference comes from matrix index contractions in the Haar averaging that connect the density matrices in a replica wormhole-like manner.

We discuss timelike surfaces of finite size in general relativity and the initial boundary value problem. We consider obstructions with the standard Dirichlet problem, and conformal version with improved properties. The ensuing dynamical features are discussed with general cosmological constant.

The S-Matrix in flat space is a naturally holographic observable. S-Matrix elements thus contain valuable information about the putative dual CFT. In this talk, I will first introduce some basic aspects of Celestial Holography and then explain how these can be inferred directly from scattering amplitudes. I will then focus on how the singularity structure of amplitudes interplays with traditional CFT structures particularly in the context of the operator product expansion (OPE) of the dual CFT. I will conclude with some discussion about the role played by supersymmetry in simplifying the putative dual CFT.
 

I will then explain that hybrid quantum-classical protocols are the most promising candidates for achieving early quantum advantage. These have the potential to solve real-world problems---including optimisation or ground-state search---but they suffer from a large number of circuit repetitions required to extract information from the quantum state. I will explain some of our recent results as hybrid quantum algorithms that exploit so-called classical shadows (random unitary protocols) in order to extract and post-process a large amount of information from the quantum computer [PRX 12, 041022 (2022)] and [arXiv:2212.11036]. I will finally identify the most likely areas where quantum computers may deliver a true advantage in the near term.

The Bethe-Gauge Correspondence (BGC) of Nekrasov and Shatashvili, linking quantum integrable spin chains to two-dimensional supersymmetric gauge theories with N=2 supersymmetry, stands out as a significant instance of the deep connection between supersymmetric gauge theories and integrable models. In this talk, I will delve into this correspondence and its origins for superspin chains. To achieve this, I will first elucidate the Bethe Side and its corresponding Gauge Side of the BGC. Subsequently, it becomes evident that the BGC can be naturally realized within String Theory. I will initially outline the brane configuration for the realization of the Gauge Side. Through the use of string dualities, this brane configuration will be mapped to another, embodying the Bethe Side of the correspondence. The 4D Chern-Simons theory plays a crucial role in this latter duality frame, elucidating the integrability of the Bethe Side. Lastly, I will elaborate on computing the main object of interest for integrable superspin chains—the R-matrix—from the BGC. While this provides a rather comprehensive picture of the correspondence, some important questions remain for further clarification. I will summarize some of the most interesting ones at the end of the talk.

In this talk, I will discuss correlation functions in 6d (2, 0) theories of two 1/2-BPS operators inserted away from a 1/2-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in AdS7×S4 in the presence of an AdS3 defect. I will show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. I will present the explicit result of all such two-point functions, which exhibits remarkable hidden simplicity.

 I will explore subtle aspects of rank-one 4d N=2 supersymmetric QFTs through their low-energy Coulomb-branch physics. This low-energy Lagrangian is famously encoded in the Seiberg-Witten (SW) curve, which is a one-parameter family of elliptic curves. Less widely appreciated is the fact that various properties of the QFTs, including properties that cannot be read off from the Lagrangian, are nonetheless encoded into the SW curve, in particular in its Mordell-Weil group. This includes the global form of the flavour group, the one-form symmetries under which defect lines are charged, and the "global form" of the theory. In particular, I will discuss in detail the difference between the pure SU(2) and the pure SO(3) N=2 SYM theories from this perspective. I will also comment on 5d SCFTs compactified on a circle in this context.

I will discuss a KLT relation of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The goal is to introduce an interesting D-brane set up in the target space in order to accommodate both quantum numbers of the closed string. I will then discuss KLT factorization of amplitudes for winding closed strings in the presence of a critical Kalb-Ramond field and the relevance of this work for nonrelativistic string theory when taking the zero Regge limit.