Domain Walls in MQCD and Monge-Ampere Equation

TL;DR

This paper investigates the representation of domain walls in MQCD as supersymmetric cycles, reducing the problem to the Monge-Ampere equation and providing formal solutions and proofs of related algebraic formulas.

Contribution

It demonstrates that the equations for U(1) invariant domain walls in MQCD can be reduced to the Monge-Ampere equation and constructs formal solutions, advancing understanding of domain walls in M-theory.

Findings

Reduction of domain wall equations to Monge-Ampere equation

Proof of algebraic formula by Kaplunovsky et al.

Construction of formal solutions for domain wall equations

Abstract

We study Witten's proposal that a domain wall exists in M-theory fivebrane version of QCD (MQCD) and that it can be represented as a supersymmetric three-cycle in G_2 holonomy manifold. It is shown that equations defining the U(1) invariant domain wall for SU(2) group can be reduced to the Monge-Ampere equation. A proof of an algebraic formula of Kaplunovsky, Sonnenschein and Yankielowicz is presented. The formal solution of equations for domain wall is constructed.