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

Marta Gomez-Reino·Stephen G. Naculich·Howard J. Schnitzer
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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.

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Marta Gomez-Reino, Stephen G. Naculich, Howard J. Schnitzer. 2005-04-27. More Pendants for Polya: Two loops in the SU(2) sector. https://doi.org/10.1088/1126-6708%2F2005%2F07%2F055

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