On holographic confining QFTs on AdS

TL;DR

This paper constructs and analyzes holographic solutions for confining quantum field theories on AdS space, revealing multiple solution types, their properties, and implications for phase structure and correlators.

Contribution

It systematically classifies regular holographic solutions for confining QFTs on AdS and analyzes their free energies and boundary conditions, introducing new solution types.

Findings

Three types of regular solutions identified

No phase transitions observed with curvature changes

Interface solutions have lower free energy than connected solutions

Abstract

Holographic quantum field theories that confine in flat space, are considered on a fixed AdS space. The space of holographic solutions for such theories is constructed and three types of regular solutions are found. Theories with two AdS boundaries provide interfaces between two confining theories. Theories with a single AdS boundary correspond to ground states of a single confining theory on AdS. We find solutions without a boundary, whose interpretation is not obvious. There is also a special limiting solution that oscillates an infinite number of times around the UV fixed point. We analyze in detail the holographic dictionary for the one-boundary solutions and compute the free energy. No (quantum) phase transitions are found when we change the curvature. We find an infinite number of pure vev solutions, but no CFT solution without a vev. We also compute the free energy of the interface solutions. We find that the product saddle points have always lower free energy than the connected solutions. This implies that in such interfaces, normalized cross-correlators vanish exponentially in $N_c^2$.