Decoupling limits of N=4 super Yang-Mills on R x S^3

Abstract

We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with gauge group SU(N). These decoupling limits lead to decoupled theories that are much simpler than the full N=4 SYM but still contain many of its interesting features. The decoupling limits correspond to being in a near-critical region, near a point with zero temperature and critical chemical potentials. The new decoupling limits are found by generalizing the limits of hep-th/0605234 to include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM but also the chemical potentials corresponding to the SO(4) symmetry. In the decoupled theories it is possible to take a strong coupling limit in a controllable manner since the full effective Hamiltonian is known. For planar N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable spin chains. We study the thermodynamics of the decoupled theories and find the Hagedorn temperature for small and large values of the effective coupling. We find an alternative formulation of the decoupling limits in the microcanonical ensemble. This leads to a characterization of certain regimes of weakly coupled N=4 SYM in which there are string-like states. Finally, we find a similar decoupling limit for pure Yang-Mills theory, which for the planar limit leads to a fully integrable decoupled theory.

48 pages, 1 figure; added references, published version

References in corpus (7)

• Phase Diagram of N=4 Super-Yang-Mills Theory with R-Symmetry Chemical Potentials
• N=4 Superconformal Characters and Partition Functions
• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3
• Matching the Hagedorn temperature in AdS/CFT
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Phase Transitions of Large N Orbifold Gauge Theories
• The Hagedorn temperature in a decoupled sector of AdS/CFT

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• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Supersymmetric Galilean Electrodynamics
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Phases of Thermal N=2 Quiver Gauge Theories
• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills