Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3

TL;DR

This paper explores the thermodynamics of N=4 Super Yang-Mills theory on RxS^3 with chemical potentials, revealing that near zero temperature and critical chemical potential, it simplifies to quantum mechanical models including spin chains and sectors related to integrability.

Contribution

It identifies three critical regions where N=4 SYM reduces to distinct quantum mechanical theories, including spin chains and sectors relevant to integrability and holography.

Findings

Near-critical N=4 SYM reduces to quantum mechanical sectors.

Identification of a spin chain limit equivalent to the Heisenberg model.

Connection between critical chemical potentials and simplified quantum theories.

Abstract

We study the thermodynamics of U(N) N=4 Super Yang-Mills (SYM) on RxS^3 with non-zero chemical potentials for the SU(4) R-symmetry. We find that when we are near a point with zero temperature and critical chemical potential, N=4 SYM on RxS^3 reduces to a quantum mechanical theory. We identify three such critical regions giving rise to three different quantum mechanical theories. Two of them have a Hilbert space given by the SU(2) and SU(2|3) sectors of N=4 SYM of recent interest in the study of integrability, while the third one is the half-BPS sector dual to bubbling AdS geometries. In the planar limit the three quantum mechanical theories can be seen as spin chains. In particular, we identify a near-critical region in which N=4 SYM on RxS^3 essentially reduces to the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find furthermore a limit in which this relation becomes exact.