Mock Modular Forms and Physics

Mock Modular Forms and Physics:

Black holes, Moonshine, and Conformal Field Theory

Objectives of Workshop

There have been exciting developments in recent years on mock modular forms and their appearance in a variety of situations in physics:

The discovery of the “Mathieu moonshine” relates the geometry of K3 surfaces to the representation theory of the Mathieu group M_24, and to a certain mock modular form. The “Umbral moonshine” phenomena generalizes this observation to a sequence of mock modular forms that are related to a corresponding sequence of finite groups, and to the 23 Niemeier lattices.

There is a fascinating interplay between the wall-crossing phenomena in supersymmetric gauge theory and string theory, and the realization of modular or automorphic symmetries in the corresponding systems. In N=4 string compactifications, the degeneracies of supersymmetric black holes have been shown to be Fourier coefficients of mock modular forms. Although some hints have been uncovered, the corresponding general story for N=2 compactifications remains to be developed.

Mock modular forms have been realized as the supersymmetric partition functions of certain non-compact superconformal field theories. These conformal field theories play a key role in the physics of black holes and black strings, and seem to be an important piece of the above puzzles.

In all these explorations, there is a feeling among the researchers that something rich and mysterious remains unknown. It seems very likely that there are underlying structures, perhaps originating in string theory, that unify these a priori different directions. These underlying structures should have implications for representation theory, number theory, geometry, gauge theory and string theory. There has already been some work on bringing these diverse developments together from both a physical and mathematical point of view, but a lot remains to be uncovered.

The idea of the workshop is to bring together people working on different aspects of these problems in an informal environment in order to share new ideas and to encourage cross-disciplinary collaborations. The workshop will have the participation of international experts working on the above topics, alongside local researchers and students who are new to the topic and wish to learn about it.

Organizers: Sujay Ashok & Sameer Murthy
This Meeting is Funded by the Department of Atomic Energy, India.