Goldstone Bosons and Global Strings in a Warped Resolved Conifold

TL;DR

This work identifies and analyzes the Goldstone mode associated with spontaneous breaking of the baryonic $U(1)_B$ in a warped resolved conifold holographically dual to the $ ext{SU}(N) imes ext{SU}(N)$ gauge theory with a diagonal VEV. By constructing a linearized RR 4-form perturbation containing the Goldstone field and introducing a closed 2-form $W$ on the warped manifold, the authors derive a finite variational problem whose minimizer encodes the Goldstone dynamics. They further show that global strings arise from D3-branes wrapping the finite $S^2$ at the conifold tip and are BPS, with tension independent of the warp factor and responsible for the required monodromy in the Goldstone field. The decay constant $f_p$ and the phase of the baryonic condensate follow from this construction, tying holographic Goldstone phenomenology to the baryonic sector of the gauge theory and offering a UV-complete description of related unparticle-like dynamics in warped throats.

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.