This week

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Topological manipulations, like gauging a finite symmetry, produce new quantum field theories from known ones. It is natural to ask how effective they are at moving one around theory space. I will sketch an appealing conjectural answer to this question in the context of 2d rational conformal field theories, which leverages ideas and techniques from 3d topological field theory. I will then present a variety of partial results in the direction of this conjecture, and physically motivate the discussion by situating it in broader quantum field theory lore.

The perturbative expansion of quantum field theory expresses physical quantities as series of numbers (or functions) associated to combinatorial graphs, called Feynman integrals. These integrals are hard to compute, and furthermore their sum forms a series that is in fact divergent. To gain insights into the large order behaviour, Feynman integrals can be approximated astonishingly well by easily computable combinatorial invariants of graphs. I will discuss two such approximations: the tropical Feynman integral and the Martin invariants, using phi^4 theory as an example. The Martin invariants are related to the O(-2) symmetric vector model and can be generalized to an integer sequence. I will end explaining how this sequence encodes the exact value of a Feynman integral through a limit used by Apery to prove the irrationality of zeta(3).

In 2+1 dimensions quantum particles can exist that are neither bosons nor fermions. Such particles, known as "anyons" have been studied theoretically for over forty years. While there has long been good reason to believe that these particles exist, particularly in fractional quantum Hall systems, it has been frustratingly difficult to perform experiments that probe the properties of these particles --- with many failures over the year. However, just in the last few years, with the maturation of a few new technologies, there have now been several very different but increasingly clear experiments that directly measure the exotic exchange statistics of these particles. I will explain the history of some of these experiments, what they have achieved, and what remains to be done.

I will describe an example of the AdS/CFT correspondence between a 4d N=1 SCFT arising from a mass deformation of N=4 SYM theory and an AdS_5 flux background of type IIB string theory. The SCFT does not admit a weakly coupled description which makes the calculation of its correlation functions challenging. Instead, I will consider a consistent trunctation of the bulk supergravity theory to explicitly compute two- and three-point correlation functions in the planar limit of the CFT. A qualitatively new feature is the presence of unprotected multiplets in the supergravity spectrum. As a non-trivial consistency check of our results, I will show agreement with superconformal Ward identities in the 4d N=1 SCFT. Based on work in progress with Nikolay Bobev.