Sp(N_c) Gauge Theories and M Theory Fivebrane

TL;DR

This paper explores the moduli space of N=1 supersymmetric Sp(N_c) gauge theories using M theory fivebranes, revealing geometric singularities and their relation to Higgs branches and dualities.

Contribution

It provides a geometric analysis of N=1 Sp(N_c) gauge theories via M theory fivebranes, connecting singularities with Higgs branches and dualities.

Findings

Identification of A_{N_f-1} and A_{2N_f-1} singularities in M theory surfaces.

Agreement of Higgs branch dimensions with brane configuration counting.

Description of vacuum expectation values matching field theory results.

Abstract

We analyze M theory fivebrane in order to study the moduli space of vacua of N=1 supersymmetric $Sp(N_c)$ gauge theories with $N_f$ flavors in four dimensions. We show how the N=2 Higgs branch can be encoded in M theory by studying the orientifold which plays a crucial role in our work. When all the quark masses are the same, the surface of the M theory spacetime representing a nontrivial ${\bf S^1}$ bundle over ${\bf R^3}$ develops $A_{N_f-1}$ type singularities at two points where D6 branes are located. Furthermore, by turning off the masses, two singular points on the surface collide and produce $A_{2N_f-1}$ type singularity. The sum of the multiplicities of rational curves on the resolved surface gives the dimension of N=2 Higgs branch which agrees with the counting from the brane configuration picture of type IIA string theory. By rotating M theory fivebranes we get the strongly coupled dynamics of N=1 theory and describe the vacuum expectation values of the meson field parameterizing Higgs branch which are in complete agreement with the field theory results. Finally, we take the limit where the mass of adjoint chiral multiplet goes to infinity and compare with field theory results. For massive case, we comment on some relations with recent work which deals with N=1 duality in the context of M theory.