Publisher’s Pick: An extremal N=2 superconformal field theory

By Phil Brown on November 14, 2017

Researchers at Stanford and Boston University construct two dimensional CFTs with the right properties to be holographic duals of three-dimensional supergravity. They spoke to Journal of Physics A: Mathematical and Theoretical about their Publisher’s Pick

Who are you?

Ethan Dyer

Liam Fitzpatrick

Nathan Benjamin

Shamit Kachru

We are Nathan Benjamin, Shamit Kachru and Ethan Dyer from Stanford University and Liam Fitzpatrick from Boston University.

What prompted you to pursue this field of research?

This work lies at the intersection of two areas: attempts to construct soluble toy models of quantum gravity or string theory, and studies of connections between special 2d quantum field theories and interesting objects in representation theory and number theory. In the former setting, it is natural to try and use the holographic correspondence between 3d AdS gravity and 2d CFT to construct gravity theories by finding 2d CFTs with very special properties. Attempts to do this have been ongoing for several years, and we realized that in the setting of N=2 supersymmetry, we could extend results of Gaberdiel, Gukov, Keller, Moore and Ooguri and construct concrete examples of theories that they had conjectured to exist. The tie to number theory and representation theory comes about because these same theories exhibit sporadic simple finite groups (in this case, M23) as symmetry groups, and their partition functions have special modular properties. This is an example of a phenomenon going under the name of “moonshine” in mathematics — referring to still mysterious ties between modular forms, representation theory, and preferred string theories.

What is this latest paper all about?

We exhibit a 2d conformal theory with the right properties (following the logic of Gaberdiel et al) to be dual to pure N=2 supergravity in AdS space with a large (almost Planckian) negative cosmological constant.

What do you plan to do next?

We are trying to generalize our methods to construct further examples of 2d CFT duals to gravity theories, now at larger central charge. The ultimate goal is to construct a tractable family of CFTs asymptoting to very large central charge, where the gravity theory becomes very weakly curved. But many obstacles remain on the path to such an example. We are in the process of borrowing tools from a cognate area of mathematics, the theory of vertex operator algebras, in hopes that they will allow us to at least extend our results from central charge c=24 to values like c=48. In a related project, we are also exploring whether the same technology might allow us to concretely construct interesting theories explaining new examples of moonshine.

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