There is a rich web of connections between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories.  I will explain an analogous relationship between quantum error-correcting codes, Lorentzian lattices, and nonchiral CFTs arising from toroidal compactifications of strings.  Specifically, I will show how quantum stabilizer codes are embedded in the operator algebras of associated Narain CFTs.   With respect to “code” CFTs, the constraints of modular invariance reduce to simple algebraic equations.  

Solving these equations provides many examples of physically distinct CFTs with the same spectrum; we also find many solutions that do not correspond to any code CFT, and likely do not correspond to any CFT at all.  This exposes a crucial limitation of the conformal bootstrap program – that in general, a solution of the bootstrap equations implies neither the existence nor the uniqueness of a corresponding CFT.  

Machine learning provides a new tool for analyzing Big Data and Small Data in mathematics and theoretical physics. In this talk, I discuss two case studies. The first predicts the volume of the knot complement of hyperbolic knots from the Jones polynomial. The second predicts the masses of baryons such as the proton and neutron from knowledge only of the meson spectrum and distinguishes between different composition hypotheses for exotic QCD resonances. Both investigations point to the existence of new analytic formulae.

Abstract:

I will explore the idea that certain theories of gravity in Anti-de

Sitter space are dual to an average over an ensemble of quantum

theories, rather than to a specific quantum theory.  I will describe

an average over Narain’s family of two-dimensional conformal field

theories which describe free bosons on a torus, and compute the

partition function using the Siegel-Weil formula.  The result takes

the form of a sum over geometries as one would expect in a theory of

gravity.  But the gravitational theory looks more like a Chern-Simons

theory than like Einstein gravity.

Zoom: https://uky.zoom.us/j/94475622713

Recording: https://uky.zoom.us/rec/share/QQujHqM5YhGd-8VMLiGw6DUPPftssuHC4vi3h_n-x27Jwbc-wBTtv5TIxvEdpxzg.EVGdktXNhdQIWDgV

We explore a possibility of constructing lattice theories from a basic principle where lattice is viewed as a restriction of the continuum. This allows us to derive a discrete derivative, nonlocal on the lattice, that satisfies Liebniz rule. As a result a theorem related to locality follows which states that any local equation in the classical continuum theory holds true also locally on the lattice. Using this one is able to preserve a remnant of all the global and gauge symmetries, which, in two dimensions, can be lifted to include local diffeomorphism and Weyl symmetries as well. Consequently, one is able, for example, to carry out classical BRST construction of covariant sting bits (for the first time).



This lattice derivative is, in some sense, similar to SLAC derivative discussed earlier in the literature. However, we point out that its action suffers from branch cut ambiguities while acting on Fourier basis. This may indicate that quantization is not straightforward and may have to be done entirely in position space.

https://uky.zoom.us/j/98298147329

Recording: https://uky.zoom.us/rec/share/DcpK6kBPxVZpLYYGq4IjzCN34vxUxAh5F1huXQEzfdMD9kDf3J6xvZJLVs_AaKLg.zG6RFkPs8EmzYdpQ

Viewing fundamental physics processes through the lenses of quantum information storage and processing is a new frontier in gravity and quantum field theory. Much of what we have learnt in the past decade builds on the notion of entanglement and its entropy. The latter quantifies how hard it is to store a quantum-many body state of interest on a classical computer. Complexity is a new player in the high-energy physics context and quantifies how hard it is to prepare a quantum-many body state using limited resources. Learning from the success story of entanglement entropy, establishing universal results on complexity in two-dimensional conformal field theories should open many new research directions, including finding a precise gravity dual. I will discuss recent progress on this problem reported in 2005.02415 and 2007.11555 with Flory.

Recording: https://uky.zoom.us/rec/share/UsIbWHaXi4DJ04EDDouJbMB0CPmJUvY0bCQSf5jIhZNJBPJE5-TTbj-Oq4NWVtYr.xSXcjGefvoy1F8o2

Abstract:

A universal relationship between asymptotic symmetries, QFT soft theorems, and low energy observables has reinvigorated attempts at flat space holography.  In this talk we introduce a map from 4d S-matrix elements to 2d correlators in the putative dual Celestial CFT.  In particular, we will focus on recent progress towards understanding elements of the IR triangle from the perspective of our Celestial CFT.

Note the unusual start time!

Recording: https://uky.zoom.us/rec/play/-Jlt4l4Zj7OW4tELdw9Yj4zi5p4rvUrm3OLcosykvV…

We explore the possibility of embedding a dS_2 universe in the interior of an asymptotically AdS_2 spacetime. We consider the problem macroscopically, discussing various constraints from gravitational models. We also discuss potential microscopic paths guided by the perspective of AdS_2 holography. 

Zoom Link : https://uky.zoom.us/j/95988631148

The trace anomaly of QCD is fundamentally important as it imparts mass to hadrons and nuclei, hence to the visible universe.

In this talk, I will introduce two recent developments regarding the anomaly. In the first part, I discuss the decomposition of the trace anomaly into the quark and gluon parts. This is a well-defined field theoretical problem that can be addressed in perturbation theory. In the second part, I will explain how to measure the gluon condensate $\lange P|F^{\mu\nu}F_{\mu\nu}|P\rangle$, which constitutes the major part of the trace anomaly, in near-threshold $J/\psi$ production in electron-proton scattering. After giving a review of the existing theoretical approaches and the experimental situation, I will explain our new approaches to both photo-production and lepto-production.

Abstract : We analyse Virasoro blocks as an expansion in heavy exchange dimension. For the one point torus block and the four point sphere block each order in the expansion can be written as polynomials in the Eisenstein series. These polynomials are further constrained to satisfy a recursion relation, which can be re-expressed as a noiseless KPZ equation for the blocks. This structure can be utilized along with the Zamolodchikov recursions to develop an algorithm to construct blocks in the heavy regime. We apply our results to find the corrections to averaged heavy-heavy-light OPE coefficients.

https://uky.zoom.us/j/99297500671

Recording: https://uky.zoom.us/rec/share/AsE8BaVwSqD1qJKmwnYn39GqIfhuLzqQjpTYGxwQB9C00GKOFaZtuuRURVNvSzTn.YsBz5vtRuhDXhbwZ

 In this talk, we review an approach to describing cosmological

physics using ordinary AdS/CFT, where the cosmological physics is the

effective description of an end-of-the-world brane which cuts off the

second asymptotic region of a two-sided black hole. The worldvolume

geometry of the brane is an FRW big-bang/big-crunch spacetime. In

favorable circumstances, the brane acts as a Randall-Sundrum Planck

brane so that gravity localizes. We describe a microscopic construction

for such an end-of-the-world brane with localized gravity in AdS/CFT,

starting from N=4 SYM theory. We suggest specific microscopic states of

N=4 SYM theory that may encode the physics in a four-dimensional

cosmological spacetime.

Recording: https://uky.zoom.us/rec/share/hSH3MH-IdlnUG-Rdjc-QO685QSPTkkCkucqtlGk-PMdgz6tQfvrT1ehlxzFpPusX.2RAdbrLBK8jGKuFo