Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

TL;DR

Spin Matrix Theory (SMT) is a novel quantum mechanical framework modeling the AdS/CFT correspondence, capturing various phases of N=4 SYM and its string theory dual through a spin chain and matrix model approach.

Contribution

The paper introduces Spin Matrix Theory as a new non-relativistic quantum model that describes near-critical points of N=4 SYM and connects to string theory in a unified framework.

Findings

SMT describes phases of N=4 SYM near zero-temperature critical points.

At large N and low temperatures, SMT reduces to spin chains resembling gauge theory.

High-temperature phases exhibit partial deconfinement and a classical matrix model regime.

Abstract

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.