A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3

Abstract

We study weakly coupled SU(N) N = 4 super Yang-Mills theory on R x S^3 at infinite N, which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighboring sites and a generalization of Polya's counting of `necklaces' (gauge-invariant operators) to include necklaces with a `pendant' (an operator which acts on neighboring beads). We find that the one-loop correction to the Hagedorn temperature is delta ln T_H = + lambda/8 pi^2.

39 pages, harvmac. v2: references and some clarifications added, v3: proof of (3.28) corrected

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• Bethe Ansatz for Quantum Strings
• Spinning strings and AdS/CFT duality
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Fine structure of Hagedorn transitions
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• Two-Loop Partition Function in the Planar Plane-Wave Matrix Model
• D-Brane Instability as a Large N Phase Transition

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