Quantum Fields and Strings

The path integral over reparametrization modes in one dimension played an important role in the duality between JT gravity and the SYK model. In this talk, I will explain that the reparametrization modes are important also in certain computations involving the string worldsheet with boundaries. A few cases in which it is expected to play a crucial role are the Wilson loop expectation value in confining string, open strings with massive endpoints, and the string dual to the half-BPS Wilson loop in N=4 supersymmetric Yang-Mills. After reviewing these cases briefly, I will focus on the last case and explain how to compute the correlation function on the BPS Wilson loop from the string worldsheet in the conformal gauge. In particular, I will show that the inclusion of the reparametrization modes is crucial for reproducing the answer obtained previously in the static gauge. I will then use the reparametrization mode path integral to study the four-point functions in the out-of-time-ordered configuration and obtain an exact answer in a double-scaling regime interpolating between the Lyapunov regime and the late-time exponential decay. Interestingly the result has exactly the same functional form as in JT gravity although the actions for the reparametrization modes are different.

Zoom link:  https://pitp.zoom.us/j/99063427266?pwd=aG5iTlczNWhxdE9xNEZoVTlMSnVOQT09

The simplest large N gauge theory is, arguably, the Gaussian matrix (or more generally, one hermitian matrix) integral. We will explicitly show that arbitrary correlators of single trace operators in this theory (without any double scaling limit) are identical to corresponding physical correlators in a dual topological string description. We will present both a novel A-model dual and also a mirror B-model Landau-Ginzburg description. The equality of correlators arises via open-closed-open string triality and a surprising relation to the c=1 string theory. The goal will be, however, to go beyond demonstrating equality but rather to make the duality manifest. For the B-model description this involves Eynard's recasting of topological recursion relations in terms of intersection numbers on moduli space. For the A-model this goes through the relation of Gaussian correlators to the special Belyi covering maps or equivalently, discrete volumes of moduli space. Finally, we also briefly mention the significance of these results for the gauge-string duality of N=4 Super Yang-Mills theory.

Zoom Link: https://pitp.zoom.us/j/93961992131?pwd=MkxlekxWU1ZGbzNZeWpzeU1TMzMrdz09

The modern point of view is that the global symmetries of a quantum field theory are described by topological defects/operators of the theory. In general such symmetries are non-invertible, i.e. the associated topological defects do not admit an inverse under fusion. I will describe a general construction of such non-invertible topological defects by coupling lower-dimensional topological quantum field theories (TQFTs) to discrete gauge fields living in a higher-dimensional bulk. The associated symmetries would be referred to as theta symmetries, as this construction can be understood as a generalization of the notion of theta angle. Mathematically, this construction is connected to interesting fusion higher-categories like those formed by higher-representations of groups and higher-groups. I will briefly explain this mathematical connection. I will also describe how the study of theta symmetries includes within it, as a special case, the study of topological phases of matter pursued in condensed matter physics. Towards the end of the talk, I will discuss some works in progress regarding possible physical applications of non-invertible symmetries. Based on ArXiv: 2212.06159, 2208.05973.

Zoom Link: https://pitp.zoom.us/j/92668739313?pwd=ZmdteFQybU9SbTlPNVQxV3l5dE5FQT09

Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more local operators with large spin compared to small spin? Using planar N=4 SYM as a testground we find a simple physical picture. Local operators do organize themselves into analytic families but the continuation of the higher families have zeroes in their structure OPE constants for lower integer spins. They thus decouple. Newton's interpolation series technique is perfectly suited to this physical problem and will allow us to explore the right complex spin half-plane.

Most people are familiar with periodic tessellations and lattices; from the floor in the PI Bistro to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their applications to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.

Zoom Link: https://pitp.zoom.us/j/91876287518?pwd=NGNLOXZHa1h1cmdnMzJxQzVMVFJJdz09

The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. I will discuss a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra. However, at loop level new poles are generated, the simplest of which are described the 1-loop effective graviton vertex. These quantum corrections violate associativity of the operator product. I will argue that this failure can be traced to an anomaly in the twistor uplift of self-dual gravity. Associativity can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.

Zoom link:  https://pitp.zoom.us/j/91979544537?pwd=Ykw4Q3lRK2ZicVhCMDhlNUxFaHhlUT09

The language of integrable systems is widely applicable to string theory. One context where it is useful is the Seiberg-Witten theory, describing low-energy dynamics of confined 4d N=2 supersymmetric gauge theories: the families of complex curves with differentials, playing a central role in this description, appeared to be spectral curves, solving the integrable systems of interacting particles. Moreover, the spectrum of stable BPS particles appears from the consideration of hyperkahler structures on the phase spaces of integrable systems. And the full partition functions of instantons, regularized by Omega-background, solve deuatonomized systems of particles.

In my talk, I will explain correspondence unifying to some extent two latter ones. It relates discrete dynamics of so-called cluster integrable systems and partition functions of 5d N=1 supersymmetric gauge theories, or more generally of topological stings on corresponding local Calabi-Yau manifolds. Based on the simplest non-trivial example, I will show how both "equations" and "solutions" sides of correspondence naturally appear in the simple statistical models of dimers and "melting crystals" made out of them.

Zoom link:  https://pitp.zoom.us/j/91449709915?pwd=eUVDeDdHVGI2ZVRwQ0hneXFpQk1wQT09

We consider four-point correlators in an arbitrary excited state of a quantum field theory.  We show that when the theory and state are holographic, such correlators can produce high-quality movies of point-like bulk particles, revealing the geometry in which they move. In some situations, Einstein’s equations amount to a local differential equation on the correlator data. In theories or states that are not holographic, images are too blurry to extract a bulk geometry. Calculations are performed by adapting formulas from conformal Regge theory, to excited states and out-of-time-order correlators.

Zoom link: https://pitp.zoom.us/j/94153545930?pwd=YUFsUW44S1Z5Ri83a2xQdEN0Vk9XZz09

One central property of the S-matrix is its invariance under field redefinitions. I will discuss how the geometry of field space makes this invariance manifest. This geometric formulation also has practical consequences. Scattering amplitudes and the renormalization group equations for a theory of scalars and gauge bosons only depend on geometric quantities. Also, the scattering amplitudes satisfy a geometric soft theorem.

Zoom link:  https://pitp.zoom.us/j/98973018515?pwd=MFJFSGM4RS9KRHFOREFBc1gvWXYwQT09

I will speak about my recent work with Vladimir Kazakov where we study the SU(Nc) lattice Yang-Mills theory in the planar limit, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on the maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, the Monte Carlo approach.

Zoom link:  https://pitp.zoom.us/j/96101268796?pwd=QkdJbm9GUzQ2YnIrM1NlcUt2Z3Nvdz09

In this talk, I will show that the action of soft graviton operators generates a w(1+infinity) symmetry in gravitational theories minimally coupled to massless and massive scalar matter in 4D asymptotically flat spacetimes.  I will discuss how the symmetry action follows from an infinite tower of soft graviton theorems in momentum space.  By generalizing the previous analyses of w(1+infinity) symmetry in massless amplitudes, these results clarify that the symmetry emerges in 4D asymptotically flat gravitational theories without any additional technical ingredients.  This talk is based on a forthcoming paper with Monica Pate. 

Zoom link:  https://pitp.zoom.us/j/91448920819?pwd=cFY0L1JPVFF2bDUwc3JiVlRlbE5ldz09

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

Zoom link:  https://pitp.zoom.us/j/96037678536?pwd=eGdhTWF3UVN1em5uZVpJbWYyM2tzUT09