One-Loop Partition Functions in Deformed $\mathcal{N}=4$ SYM Theory

TY - JOUR

T1 - One-Loop Partition Functions in Deformed $\mathcal{N}=4$ SYM Theory

AU - Fokken, Jan

AU - Wilhelm, Matthias

PY - 2015

Y1 - 2015

N2 - We study the thermodynamic behaviour of the real $\beta$- and $\gamma_i$-deformation of $\mathcal{N}=4$ Super Yang-Mills theory on $\mathbb{R}\times S^3$ in the planar limit. These theories were shown to be the most general asymptotically integrable supersymmetric and non-supersymmetric field-theory deformations of $\mathcal{N}=4$ Super Yang-Mills theory, respectively. We calculate the first loop correction to their partition functions using an extension of the dilatation-operator and P\'{o}lya-counting approach. In particular, we account for the one-loop finite-size effects which occur for operators of length one and two. Remarkably, we find that the $\mathcal{O}(\lambda)$ correction to the Hagedorn temperature is independent of the deformation parameters, although the partition function depends on them in a non-trivial way.

AB - We study the thermodynamic behaviour of the real $\beta$- and $\gamma_i$-deformation of $\mathcal{N}=4$ Super Yang-Mills theory on $\mathbb{R}\times S^3$ in the planar limit. These theories were shown to be the most general asymptotically integrable supersymmetric and non-supersymmetric field-theory deformations of $\mathcal{N}=4$ Super Yang-Mills theory, respectively. We calculate the first loop correction to their partition functions using an extension of the dilatation-operator and P\'{o}lya-counting approach. In particular, we account for the one-loop finite-size effects which occur for operators of length one and two. Remarkably, we find that the $\mathcal{O}(\lambda)$ correction to the Hagedorn temperature is independent of the deformation parameters, although the partition function depends on them in a non-trivial way.

KW - hep-th

KW - hep-lat

KW - hep-ph

U2 - 10.1007/JHEP03(2015)018

DO - 10.1007/JHEP03(2015)018

M3 - Journal article

SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 03

M1 - 018

ER -