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

Abstract

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 Pólya-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.

arXiv comment31 pages, LaTeX, BibTeX, feynmp; v2: 32 pages, references added, typos corrected, matches published version

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Cited by in corpus (4)

• The Hagedorn temperature of AdS5/CFT4 via integrability
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• 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