Two-dimensional gauge theories, intersection numbers and special functions

Abstract: The partition function of two dimensional Yang-Mills theory contains a wealth of information about the moduli space of connections on surfaces. We study this problem on a special class of surfaces of infinite genus, which are constructed recursively. While the results are suggestive of an underlying geometrical structure, we use it as a prop to efficiently compute results for finite genus surfaces. Riemann zeta function, confluent hypergeometric function and its truncations show up in explicit computations for the gauge group SU(2). Much of the corresponding results are open for other groups.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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