Confinement in Anti-de Sitter Space

TL;DR

The paper analyzes confinement of four-dimensional gauge theories on AdS${}_4$, revealing that AdS curvature provides an infrared cutoff and introduces a dimensionless control parameter $oldsymbol{\Lambda L}$ that governs a zero-temperature quantum phase transition between deconfined and confined regimes. It maps out multiple confinement scenarios in fixed AdS$_4$ (including boundary-condition effects and finite-temperature behavior) and then extends the discussion to dynamical gravity, where the bulk corresponds to a large-$\hat{N}$ CFT$_3$ and confinement signatures must be read in the dual theory. The work also explores how supersymmetric theories ($\mathcal{N}=1,2,4$) behave in AdS$_4$, highlighting how boundary conditions alter vacua structure, holomorphy, and possible confinement mechanisms, including insights from Seiberg–Witten theory and S-duality. Overall, the paper provides a framework for understanding confinement in curved spacetime and its holographic manifestations, with implications for identifying bulk confinement through dual CFT$^{\!}_3$ observables and for string-theory realizations of AdS gauge dynamics.

Abstract

Four dimensional gauge theories in anti-de Sitter space, including pure Yang-Mills theory, exhibit a quantum phase transition between a deconfined phase and a confined phase as the gauge coupling is varied. We explore various mechanisms by which this may occur, both in a fixed background and in the presence of gravity. We also make a number of observations on the dynamics of four dimensional supersymmetric gauge theories in anti-de Sitter space.