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

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.

33 pages, 3 figures. v2,v3: typos fixed, refs added, minor changes in sec. 3, formulas corrected in sec. 6. v4: typos fixed

References in corpus (3)

• Phase Diagram of N=4 Super-Yang-Mills Theory with R-Symmetry Chemical Potentials
• Fine structure of Hagedorn transitions
• Quantum Mechanics of Lowest Landau Level Derived from N=4 SYM with Chemical Potential

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