Room: 0089
Instytut Matematyki, ul. Łojasiewicza 6, 30-348 Kraków
Gábor Etesi
(Budapesti Műszaki és Gazdaságtudományi Egyetem,
Hungary)
An S-duality check in Abelian gauge theory over asymptotically locally flat spaces
Abstract:
In this talk we examine the modular properties of the partition function of Maxwell
theory formulated over asymptotically locally flat (ALF) spaces such as the
Riemannian Schwarzschild, Kerr and multi-Taub-NUT geometries.
We make the following two observations:
(i) Using zeta-function regularization to calculate the partition function we run
into difficulties because the spectrum of the Laplacian is continuous in our case.
However based on an idea of Witten we can calculate the partition function and
comparing it with the zeta-function approach we obtain non-trivial predictions for
the zeta-function of the Laplacian over these non-compact spaces.
(ii) Secondly, we find that the naive theory fails to possess modular invariance; this
however can be restored by adding new terms to the Lagrangian describing the
dynamics of gravity as expected.