Jul 3 – 8, 2016
The University of Melbourne
Australia/Melbourne timezone

Supersymmetry, multi-instantons, and the necessity of Lefshetz thimbles

Jul 7, 2016, 2:00 PM
Alice Hoy Room 333

Alice Hoy Room 333

Talk Formal Field and String Theory Formal Field and String Theory


Erich Poppitz


Studies of four-dimensional confining supersymmetric theories on $R^3\times S^1$ have shown, via the power of supersymmetry, that instanton-antiinstanton "topological molecules" have profound effects on their vacuum structure. In the calculable semiclassical regime, these are found responsible for center stability, confinement, and discrete chiral symmetry breaking. These configurations also play crucial role in recent studies of "resurgence"-the fascinating interplay of perturbative and nonperturbative physics. They also exist in nonsupersymmetric theories, but their identification has been hampered by the lack of a controlled way to distinguish them from the perturbative vacuum.

We shall argue, using non-supersymmetric path integral methods, that the inclusion of instanton-antiinstanton configurations in the path integral requires the use of "Lefshetz thimbles", i.e. the complexification of (at least some) the integration paths in field space. We show that the corresponding results agree with those predicted by supersymmetry and discuss avenues for current and future work.

Primary author

Erich Poppitz

Presentation materials