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

TL;DR

This paper computes the exact one-loop partition function of N=4 super Yang-Mills theory on R x S^3 at large N, revealing a correction to the Hagedorn temperature using a novel necklace counting method with a pendant.

Contribution

It introduces a generalized Polya counting method with a pendant to calculate the one-loop partition function of N=4 SYM on R x S^3 at infinite N.

Findings

Exact one-loop partition function below Hagedorn temperature

One-loop correction to Hagedorn temperature: delta ln T_H = + lambda/8 pi^2

Method employs spin chain Hamiltonian and necklace counting with pendant

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.