Past String Theory Seminar

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.