Quantum Fields and Strings

In this talk, I examine the massless 't Hooft equation. This integral equation governs meson bound state wavefunctions in 2D SU(N) gauge theory in the large-N limit, and it can also be obtained by quantizing a folded string in flat space. The folded string is a limiting case of a more general setup: a four-segmented string moving in three-dimensional anti-de Sitter (AdS) space. I compute its classical spectral curve using celestial variables and planar bipartite graphs, also known as on-shell diagrams or brane tilings. In this more general setup, the 't Hooft equation acquires an extra term, which has previously been proposed as an effective confining potential in QCD. After an integral transform, the equation can be inverted in terms of a finite difference equation. I show that this difference equation has a natural interpretation as the quantized (non-analytic) spectral curve of the string. The spectrum interpolates between equally spaced energy levels in the tensionless limit and 't Hooft's nearly linear Regge trajectory at infinite AdS radius.

Zoom link:  https://pitp.zoom.us/j/97373882483?pwd=NmphN0N3ckdHbHdlcVpKcGkzMHY1Zz09

Chern-Simons theories can possess 't Hooft anomalies for time-reversal symmetry. In this talk, we will discuss abelian Chern-Simons theories with an interesting time-reversal symmetry algebra and compute the classification of the anomaly, which is captured by a bordism group. In order to get the classification correct I will explain the argument we used that utilized the Smith homomorphism for bordism groups. In order to compute the value of the anomaly we study the Atiyah-Hirzebruch spectral sequence and find a way to trivialize each layer of the anomaly. I will also discuss the generating manifold for the corresponding bordism group, and how it arises from the Smith homomorphism. The knowledge of this manifold allows one to compute the partition function by using the data that characterizes the Chern-Simons theory and the symmetry actions; this gives a robust check of our answer for the anomaly. This is based on work in progress with Arun Debray and Weicheng Ye. 

Zoom link:  TBA

Dynamical fixed points are late-time attractors of interactive QFTs that differ from thermal equilibria by a constant entropy production rate. We use holographic framework to analyze such fixed points of strongly coupled gauge theories, driven by homogeneous and isotropic expansion of the background metric - equivalently, a late-time dynamics of a corresponding QFT in Friedmann-Lemaitre-Robertson-Walker Universe. As an application, we discuss gravitational reheating of quark-gluon plasma in the exit from the early-cosmology inflation.

Zoom link:  https://pitp.zoom.us/j/96385064629?pwd=NTZrdUdtbW0rZkxPdFZ3ZnZRUzhjZz09

Scattering amplitudes are where quantum field theory directly meets collider experiments.  An excellent model for scattering in QCD is provided by N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors, where the theory becomes integrable.  The first nontrivial amplitude in this theory is for 6 gluons.  It can be computed to 7 loops using a bootstrap based on the rigidity of the function space of multiple polylogarithms, together with a few other conditions.  One can also bootstrap a particular form factor, for the chiral stress-tensor operator to produce 3 gluons, through 8 loops.  This form factor is the N=4 analog of the LHC process, gluon gluon --> Higgs + gluon. Remarkably, the two sets of results are related by a mysterious `antipodal' duality, which exchanges the role of branch cuts and derivatives.  Furthermore, this duality is `explained' by an antipodal self-duality of the 4 gluon form factor of the same operator; although it is still fair to say of the self-duality, `who ordered that?'

Zoom link:  https://pitp.zoom.us/j/96265005656?pwd=Qndza3pIKzdmZVJGL0s1ZUZkRmp4QT09

In massless QED, we find that the classical U(1) axial symmetry is not completely broken by the Adler-Bell-Jackiw anomaly. Rather, it is resurrected as a generalized global symmetry labeled by the rational numbers. Intuitively, this new global symmetry in QED is a composition of the naive axial rotation and a fractional quantum Hall state. The conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra. We further generalize our construction to QCD, and show that the neutral pion decay can be derived from a matching condition of the non-invertible global symmetry. Finally, we find a non-invertible Gauss law in axion-Maxwell theory.

Zoom link:  https://pitp.zoom.us/j/93832561140?pwd=czFFSkVvYS9RbXRjOTJPQVFhL2hGZz09

In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

Zoom link:  https://pitp.zoom.us/j/97435154387?pwd=OHYrRW9uSW5VeHRFUld1dmtVbmJiZz09

I will use the S-matrix Bootstrap to carve out the space of unitary, crossing symmetric, and supersymmetric graviton scattering amplitudes in nine, ten, and eleven dimensions. I will introduce a novel extension of positivity for massless particles beyond the forward limit called “positivity in the sky” that significantly improves the convergence of the bootstrap algorithm.

I will show the bounds on the first leading correction to maximal supergravity, study the physics of the extremal amplitudes and compare them with the available nonperturbative String and M-theory results.

Zoom link:  https://pitp.zoom.us/j/99182927406?pwd=bWxIazFvUzhVQkpBdWluZURIM21wUT09

In this talk I will show the equivalence of several different tests of the Jacobi identity for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT. Along the way I will clarify the role of the order of soft and collinear limits in obstructing the Jacobi identity for soft insertions and I will argue that, despite their current-algebra-like properties, soft insertions as formulated in this talk cannot be interpreted as local operators in celestial conformal field theory.

Zoom link:  https://pitp.zoom.us/j/99642885302?pwd=dWZhbzZUYnBuSlJ3UzBhSHdqdzVKdz09

We identify the microstates of the non–supersymmetric, asymptotically flat 2$d$ black hole in the dual $c=1$ matrix quantum mechanics (MQM). We calculate the partition function of the theory using Hamiltonian methods and reproduce one of two conflicting results found by Kazakov and Tseytlin. We find the entropy by counting states and the energy by approximately solving the Schrodinger equation. The dominant contribution to the partition function in the double-scaling limit is a novel bound state that can be considered an explicit dual of the black hole microstates. This bound state is long-lived and evaporates slowly, exactly like a black hole in asymptotically flat space.

Based on arXiv:2210.11493

Zoom link:  https://pitp.zoom.us/j/96045839335?pwd=S3NXQ2ZsdUlaSWpIVHoxTk11NUxtdz09

I will revisit the physics of Heterotic Strings on four-dimensional ADE singularities in light of recent progress in the context of higher global symmetries combined with our improved understanding of 6d SCFTs over the past decade. In particular, on ADE singularities the fractional heterotic little string instantons enjoy a continuous 2 group symmetry that one can exploit to constrain possible networks of T-dualities. These predictions are confirmed exploiting duality with F-theory, and also shed light on the question of the geometric engineering limit of heterotic strings on ALE spaces. Based on joint works with Kantaro Ohmori, Paul-Konstantin Öhlmann and Muyang Liu.

Zoom Link: https://pitp.zoom.us/j/92559165562?pwd=R3NLRktuWFYyKzFNQmhFeS9sQ2tQZz09

Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/95685877198?pwd=ZVhaRmMrQ1VNcXNVOEpTOHVTd1F6QT09

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