Theory HEP Seminar

S-Duality, Janus Configurations and Quadratic Reciprocity

Ori Ganor

Berkeley

By studying the partition function of a Janus configuration (Super-Yang-Mills theory with a variable coupling constant) with S-duality twisted boundary conditions, one obtains the Landsberg-Schaar relation, which is an identity involving finite sums of roots of unity. It is related to Quadratic Reciprocity, which is the famous connection between the problems of “does p have a square root, modulo q” and “does q have a square root, modulo p”. The derivation employs U(1) gauge group, and I will comment on extensions of these ideas to nonabelian gauge groups.