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

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.

15 pages

References in corpus (11)

• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Spinning strings and AdS/CFT duality
• A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Finite temperature effective action, AdS_5 black holes, and 1/N expansion
• Deconfinement in Matrix Models about the Gross--Witten Point
• Spin chain sigma models with fermions
• A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3
• Fine structure of Hagedorn transitions
• Free Energy and Phase Transition of the Matrix Model on a Plane-Wave
• Two-Loop Partition Function in the Planar Plane-Wave Matrix Model

Cited by in corpus (14)

• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3
• Matching the Hagedorn temperature in AdS/CFT
• Random walks and the Hagedorn transition
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• From Free Fields to AdS -- Thermal Case
• Hagedorn divergences and tachyon potential
• Flavour singlets in gauge theory as Permutations
• The Morphology of N=6 Chern-Simons Theory
• The 2-loop partition function of large N gauge theories with adjoint matter on S^3
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Refined Counting of Necklaces in One-loop $\mathcal{N}=4$ SYM
• One-Loop Partition Functions in Deformed $\mathcal{N}=4$ SYM Theory
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations