Week 13.11.2022 – 19.11.2022

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

In some ways the ocean acts like a topological insulator. There are chiral edge modes, localised at the coast, that go clockwise in the Northern hemisphere and anti-clockwise in the Southern hemisphere. I’ll describe these features and explain how this can be understood in terms of something more familiar to high energy physicists. I’ll show that the equations that govern the long-time dynamics of the ocean can be recast as a Maxwell-Chern-Simons theory.

According to the correspondence principle, classical physics emerges in the limit of large quantum numbers. We examine two examples of the semiclassical description of conformal field theory data: large spin impurities in the free triplet scalar field theory and large charge Wilson lines in QED. By simultaneously taking the coupling to zero and quantum numbers to infinity, we can connect the microscopic to the emergent classical description smoothly.

Mixed anomalies and generalized symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories (QFTs). A natural question is whether these are related in any way to certain supersymmetric partition functions or indices, which have also been used extensively to study the dynamics of QFTs. In this talk, we address this question in the context of 3d N≥3 gauge theories using the superconformal index. In particular, using the index we are able to detect mixed anomalies involving discrete 0-form global symmetries, and possibly a 1-form symmetry. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, the T(SU(N)) theory of Gaiotto-Witten and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries involved in mixed anomalies of some of these models and using constructions available in the literature, we obtain various interesting theories with two-group structures or non-invertible symmetries.

Results in Quantum Field Theories, such as anomalous dimensions or scattering amplitudes are known to exhibit rich properities under the Galois coaction that acts on period integrals. I will show how these phenomena arise directly from an integrability setup describing certain anomalous dimensions of an integrable four-dimensional scalar model. I will also discuss a conjectural all-loop differential equation for these quantities, constructed from derivatives with respect to Riemann zeta values.