Goldstone Bosons and Global Strings in a Warped Resolved Conifold

TL;DR

This paper explores the duality between a warped resolved conifold background in type IIB string theory and a supersymmetric gauge theory, focusing on the Goldstone boson arising from symmetry breaking and its associated global strings.

Contribution

It explicitly constructs the Goldstone boson perturbation and identifies the global strings as D3-branes wrapping the conifold's two-cycle.

Findings

Goldstone boson perturbation explicitly constructed

Global strings identified as D3-branes wrapping the two-cycle

Connections established between geometric resolution and symmetry breaking

Abstract

A warped resolved conifold background of type IIB theory, constructed in hep-th/0701064, is dual to the supersymmetric $SU(N)\times SU(N)$ gauge theory with a vacuum expectation value (VEV) for one of the bifundamental chiral superfields. This VEV breaks both the superconformal invariance and the baryonic symmetry. The absolute value of the VEV controls the resolution parameter of the conifold. In this paper we study the phase of the VEV, which corresponds to the Goldstone boson of the broken symmetry. We explicitly construct the linearized perturbation of the 4-form R-R potential that contains the Goldstone boson. On general grounds, the theory should contain global strings which create a monodromy of the pseudoscalar Goldstone boson field. We identify these strings with the $D3$-branes wrapping the two-cycle at the tip of the warped resolved conifold.