Alladi Ramakrishnan Hall

Towards a classification of two-character conformal field theories

Sunil Mukhi

IISER, Pune

In the first talk I will give a brief survey of rational conformal field theories in two dimensions, including the interesting case of meromorphic theories. Thereafter I will review a method pioneered in 1988 by Mathur, Sen and myself for the classification of rational CFT. The relevant results obtained by us for two- and three-character theories, as well as more recent work in 2015-2017, will be summarised. In the second talk I will start by highlighting relevant works of Kaneko-Zagier and other mathematicians, and then describe the results of my paper arXiv:1810.09472 which uses these to provide a complete classification of admissible characters for the two-character case. I will conclude by discussing the problem of identifying whether a pair of characters actually corresponds to a conformal field theory, and if so, how to construct the theory. This part is based on arXiv: 1812.05109.