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

We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on ℝ × 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. © SISSA 2005.