Off-shell M5 Brane, Perturbed Seiberg-Witten Theory, and Metastable Vacua

TL;DR

This paper shows how off-shell M5-brane actions can model the scalar potential of perturbed Seiberg-Witten theories, revealing insights into metastable vacua and their stability through geometric configurations.

Contribution

It constructs exact nonholomorphic M5 configurations for SU(2) Seiberg-Witten theory with a superpotential, connecting to metastable vacua and providing geometric intuition.

Findings

M5-brane captures scalar potential of perturbed Seiberg-Witten theory

Exact nonholomorphic M5 solutions correspond to metastable vacua

Geometric analysis offers insight into vacuum stability

Abstract

We demonstrate that, in an appropriate limit, the off-shell M5-brane worldvolume action effectively captures the scalar potential of Seiberg-Witten theory perturbed by a small superpotential and, consequently, any nonsupersymmetric vacua that it describes. This happens in a similar manner to the emergence from M5's of the scalar potential describing certain type IIB flux configurations [arXiv:0705.0983]. We then construct exact nonholomorphic M5 configurations in the special case of SU(2) Seiberg-Witten theory deformed by a degree six superpotential which correspond to the recently discovered metastable vacua of Ooguri, Ookouchi, Park [arXiv:0704.3613], and Pastras [arXiv:0705.0505]. These solutions take the approximate form of a holomorphic Seiberg-Witten geometry with harmonic embedding along a transverse direction and allow us to obtain geometric intuition for local stability of the gauge theory vacua. As usual, dynamical processes in the gauge theory, such as the decay of nonsupersymmetric vacua, take on a different character in the M5 description which, due to issues of boundary conditions, typically involves runaway behavior in MQCD.