More Pendants for Polya: Two loops in the SU(2) sector

TL;DR

This paper extends computational methods to analyze the two-loop dilatation operator in the SU(2) sector of N=4 super Yang-Mills theory, calculating the partition function and Hagedorn temperature to explore potential stringy behavior.

Contribution

It introduces a novel approach to compute the partition function for a non-nearest neighbor spin-chain Hamiltonian in the SU(2) sector at two loops.

Findings

Calculated the partition function for the SU(2) sector at two loops.

Determined the Hagedorn temperature indicating the density of states.

Suggested potential stringy behavior in the dual theory.

Abstract

We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on R x S^3 in which the dilatation operator is represented by a spin-chain Hamiltonian acting on pairs of states, not necessarily nearest neighbors. A specific application of this is the two-loop dilatation operator of the planar SU(2) subsector of the N=4 SU(N) super Yang-Mills theory in the large-N limit. We compute the partition function and Hagedorn temperature for this sector to second order in the gauge coupling. The Hagedorn temperature is to be interpreted as giving the exponentially-rising portion of the density of states of the SU(2) sector, which may be a signal of stringy behavior in the dual theory.