Symmetry-breaking vacua and baryon condensates in AdS/CFT

TL;DR

This work analyzes symmetry-breaking vacua in AdS/CFT for Type IIB string theory on $AdS_5\times Y$ with Sasaki–Einstein $Y$, focusing on simultaneous breaking of conformal and baryonic symmetries. It builds a detailed correspondence between the gauge theory vacuum moduli space and the gravity moduli space of flat RR/B fields on asymptotically conical Calabi–Yau manifolds, and decomposes linearly fluctuating moduli into Goldstone modes for non-anomalous baryonic $U(1)$s and potential modes for anomalous ones. The authors establish a concrete prescription for computing baryon condensates via Euclidean D3-branes with fixed boundary data, including a topological action, large gauge transformation consistency, and a summation over worldvolume instantons that yields a theta-function structure. They show how RR and metric moduli couple to Goldstone and pseudo-Goldstone bosons, tying the holographic currents to KK modes of the gravity background and clarifying the role of crepant resolutions in the dual descriptions. The framework provides a geometric bridge between gravity moduli, KK spectra, and baryonic VEVs in holographic vacua, offering a pathway to test AdS/CFT predictions and to count baryonic operators in quiver gauge theories.

Abstract

We study the gravity duals of symmetry-breaking deformations of superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5 x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau manifolds, and match this to the gauge theory vacuum moduli space. We discuss certain linearised fluctuations of the moduli, identifying the Goldstone bosons associated with spontaneous breaking of non-anomalous baryonic symmetries. The remaining moduli fields are related to spontaneous breaking of anomalous baryonic symmetries. We also elaborate on the proposal that computing condensates of baryon operators is equivalent to computing the partition function of a non-compact Euclidean D3-brane in the background supergravity solution, with fixed boundary conditions at infinity.