Publisher’s Pick: new perspectives on mysterious theories

By Thomas Farrell on December 9, 2016

We talk to Dr Matthew Buican and Dr Takahiro Nishinaka about their recent work published in Journal of Physics A.

Dr Takahiro Nishinaka

Dr Matthew Buican

Who are you?

We are Dr. Matthew Buican of Queen Mary University of London in the United Kingdom and Dr. Takahiro Nishinaka of the Yukawa Institute for Theoretical Physics in Kyoto, Japan.

What prompted you to pursue this field of research?

We were both fascinated by a set of mysterious quantum field theories (QFTs) called Argyres-Douglas (AD) theories. These QFTs were discovered over two decades ago by the eponymous Philip Argyres and Michael Douglas (the great physicist, not the actor!) who thought of these theories as realizing Dirac’s old idea of a QFT containing fundamental electrons and monopoles in a consistent way (that is to say, without needing to appeal to any additional short-distance “completion” of the theory).

For a long time, such theories seemed to be simultaneously simple (in the sense of having few “degrees of freedom”) and, at the same time, very difficult to describe properly (important aspects of their spectra were completely mysterious). Finally, building on work of Gadde, Rastelli, Razamat, and Yan, we found a way to get a new perspective on these theories that has begun to clarify the precise ways in which these theories are simple and the ways in which they are subtle.

What is this latest paper all about?

This paper is about taking the above AD theories and thinking of them in a space-time with three non-compact directions and one compact direction (a circle). The corresponding three-dimensional theories that you get at energies small compared to the inverse radius of the compact dimension are incredibly simple as well (for the theories we are studying in this paper, they can be described as long-distance limits of three-dimensional abelian gauge theories). Moreover, they can be studied using well-known Lagrangian techniques. Combined with some of the insights we had into the four-dimensional parent theories, we were able to use these three-dimensional Lagrangian descriptions to see how certain partition functions encode aspects of the original Coulomb branch physics studied when AD theories were first discovered. But this time, we are beginning to see how this physics fits into a bigger structure. Moreover, our study of the three dimensional theories gives us confidence we understand what goes on in four dimensions.

What do you plan to do next?

Our work points to a union of the ideas of chiral algebras (due in this context to Beem, Lemos, Liendo, Peelaers, Rastelli, and van Rees) with the work of Seiberg and Witten on the Coulomb branch of N=2 theories from the mid 90’s. We would like to understand this new edifice better (interestingly, almost simultaneous work of Cordova and Shao came to a similar conclusion using a radically different approach).

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