Magnetic Heisenberg-chain/pp-wave correspondence

Abstract

We find a decoupling limit of planar N=4 super Yang-Mills (SYM) on R x S^3 in which it becomes equivalent to the ferromagnetic XXX_{1/2} Heisenberg spin chain in an external magnetic field. The decoupling limit generalizes the one found in hep-th/0605234 corresponding to the case with zero magnetic field. The presence of the magnetic field is seen to break the degeneracy of the vacuum sector and it has a non-trivial effect on the low energy spectrum. We find a general connection between the Hagedorn temperature of planar N=4 SYM on R x S^3 in the decoupling limit and the thermodynamics of the Heisenberg chain. This is used to study the Hagedorn temperature for small and large value of the effective coupling. We consider the dual decoupling limit of type IIB strings on AdS_5 x S^5. We find a Penrose limit compatible with the decoupling limit that gives a magnetic pp-wave background. The breaking of the symmetry by the magnetic field on the gauge theory side is seen to have a geometric counterpart in the derivation of the Penrose limit. We take the decoupling limit of the pp-wave spectrum and succesfully match the resulting spectrum to the low energy spectrum on the gauge theory side. This enables us to match the Hagedorn temperature of the pp-wave to the Hagedorn temperature of the gauge theory for large effective coupling. This generalizes the results of hep-th/0608115 to the case of non-zero magnetic field.

35 pages, 2 figures. v2: Refs. added

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• N=4 SYM on S^3 with Near Critical Chemical Potentials
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Aspects of Non-Relativistic Quantum Field Theories
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• The Panorama of Spin Matrix Theory
• Finite-size corrections to the rotating string and the winding state
• Thermodynamics of theories with sixteen supercharges in non-trivial vacua
• The 2-loop partition function of large N gauge theories with adjoint matter on S^3
• New Penrose Limits and AdS/CFT
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
• Phases of Thermal N=2 Quiver Gauge Theories
• 2D Heisenberg model from rotating membrane
• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials
• Aspects of Gauge-Gravity Duality