QCD in AdS

TL;DR

This paper investigates how boundary conditions and matter content in AdS space influence the behavior of QCD-like theories, revealing mechanisms for boundary CFT disappearance and the role of operators in conformal and confining phases.

Contribution

It extends previous pure Yang-Mills results to include matter fields, analyzing anomalous dimensions and boundary conditions to understand phase transitions and boundary CFT dynamics.

Findings

Anomalous dimensions depend on boundary conditions, negative for Dirichlet, positive for Neumann.

In the conformal window, an operator becomes the displacement operator with zero anomalous dimension.

Discussions on boundary conditions relate to chiral symmetry breaking in flat space.

Abstract

We study QCD on AdS space with scalars or fermions in the fundamental representation, extending earlier results on pure Yang-Mills theory. In the latter, the Dirichlet boundary condition is conjectured to disappear via merger and annihilation, as signaled by the lightest scalar singlet operator approaching marginality as the coupling increases. With matter, there are two candidate operators for this mechanism. We compute their one-loop anomalous dimensions via broken conformal Ward identities and Witten diagrams. In the confining phase, with Dirichlet (Neumann) boundary condition, their anomalous dimensions are negative (positive), consistent with the disappearance (persistence) of the associated boundary CFT in the flat-space limit. In the conformal window, one of these operators becomes the displacement operator of the IR CFT, as signaled by the vanishing of its one-loop anomalous dimension in the perturbative Banks-Zaks regime. Possible scenarios for the lower edge of the conformal window are discussed. Finally, we consider general boundary conditions on fermions and discuss their relation to chiral symmetry breaking in flat space.