Quantum Fields and Strings

We develop the bulk geometric description of correlation functions of operators whose scaling dimensions are of order the central charge in AdS/CFT. We follow a bottom-up approach, discussing solutions to Einstein gravity that are closely related to familiar black holes in AdS. In order to reproduce the correct dependence of a conformal correlation function on the location of operator insertions, we must introduce a novel Gibbons-Hawking-York boundary term associated with the stretched horizon of each black hole. We discuss the bulk dual of two point functions in CFT’s living in arbitrary dimensions. Specializing to AdS3 allows us to discuss higher point functions, where we find that the dual geometries are sometimes multi-boundary wormholes, whose holographic interpretation has been the focus of much recent activity.

Zoom Link: TBD

I will construct a top-down example of celestial holography, based on recent work with Costello and Paquette. Our duality relates certain models of self-dual gauge theory and conformal gravity, placed on an asymptotically flat four dimensional spacetime called Burns space, to a two dimensional chiral algebra living on D1-branes in a topological string theory on twistor space.

Zoom link:  https://pitp.zoom.us/j/92898535744?pwd=T2w2SUp0VnU5NWtPSm50VENvWlRYQT09

Gravity is exciting from both theoretical and observational perspectives. In this talk, I will discuss how gravitational observables, such as waveforms, can be determined from scattering amplitudes in quantum field theory. We can therefore use the full arsenal of theoretical collider physics to compute gravitational waveforms. As an example, I will describe the waveform generated in a scattering process at next-to-leading order. I will finish by discussing how amplitudes can further be used to understand non-radiative aspects of gravity, including the curvature of the Kerr metric itself. This leads to a network of “double copy” relations between classical solutions of the Maxwell and Einstein equations.

Zoom link:  https://pitp.zoom.us/j/92038383246?pwd=RjQwVHo1VWR6VDl0a3VPZEU0ZXFyUT09

A new approach for the first quantization of superstrings, called B-RNS-GSS formalism, is being constructed. It consists of quantizing embeddings of super surfaces into superspaces. As in the classical theory of super-embeddings, it has twistor-like variables. In this talk, besides motivating the need for such a formalism, I will review the work done in hep-th: 2211.06899, where the hetetoric supergravity equations of motion were derived from BRST nilpotency.

Zoom link:  https://pitp.zoom.us/j/98656433153?pwd=NjlpcUtITDAwWlgycUtUZUVsZ3QrQT09

Taking string theory off shell requires breaking Weyl invariance on the worldsheet, i.e. the worldsheet theory is now a QFT instead of a CFT. I will explain Tseytlin’s first-quantized approach to taking the worldsheet theory off-shell in a consistent manner, with a particular emphasis on the subtleties involved in calculating the sphere amplitude. This approach allows for the derivation of a classical string action which gives rise to the correct equations of motion and S-matrix, to all orders in perturbation theory. 

I'll also explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show explicitly how the classical (tree-level) effective action and entropy S = A/4G_N may be calculated from the sphere diagrams. 

Time permitting, I will discuss ongoing efforts to derive the Ryu-Takayanagi formula in string theory.

Based on arXiv:2211.08607 and arXiv:2211.16448. 

Zoom link:  https://pitp.zoom.us/j/93668017324?pwd=K2pxZEhjalRTWkVVbVRESCtRVDFmUT09

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