Thermodynamics of Large-N Super Yang-Mills Theory and AdS/CFT Correspondence

TL;DR

This paper investigates the thermodynamics of N=4 super Yang-Mills theory across weak and strong coupling regimes, using perturbative and Pade approximant methods to suggest a smooth interpolation consistent with AdS/CFT predictions.

Contribution

It provides a detailed analysis of the free-energy corrections and employs Pade approximants to connect weak and strong coupling thermodynamics in N=4 SYM.

Findings

Leading and next-to-leading order corrections have opposite signs.

Pade approximants suggest a monotonic decrease in free-energy with increasing coupling.

Results support a smooth thermodynamic transition consistent with AdS/CFT.

Abstract

Thermodynamics of d=4, N=4 supersymmetric SU(N) Yang-Mills theory is studied with particular attention on perturbative expansion at weak `t Hooft coupling regime and interpolation to strong coupling regime thereof. Non-ideal gas effect to free-energy is calculated and found that leading- and next-to-leading-order corrections contribute with relative opposite sign. Pade approximant method is adopted to improve fixed-order, perturbative series and is found to decrease free-energy monotonically as `t Hooft coupling parameter is increased. This may be regarded as an indication of smooth interpolation of thermodynamics between weak and strong `t Hooft coupling regimes, as suggested by Maldacena's AdS/CFT correspondence.