One-loop partition functions in deformed N = 4 $$ \mathcal{N}=4 $$ SYM theory

Abstract

We study the thermodynamic behaviour of the real β-and γ i -deformation of N = 4 Super Yang-Mills theory on R×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 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 oneloop finite-size effects which occur for operators of length one and two. Remarkably, we find that the O(λ) correction to the Hagedorn temperature is independent of the deformation parameters, although the partition function depends on them in a nontrivial way.

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

“…This could provide a connection to the cases of the Hagedorn temperature in the pp-wave or spin-matrix-theory limits [34][35][36][37][38][39][40][41][42][43]. Moreover, it would be interesting to consider the Hagedorn temperature for integrable deformations of N = 4 SYM theory (see [44] for one-loop results) and for the three-dimensional N = 6 superconformal Chern-Simons theory, for which a QSC formulation for the spectral problem exists as well [45]. In particular, it would be intriguing to study what happens at strong coupling in these cases.…”

Amplitudes, form factors and the dilatation operator in N = 4 $$ \mathcal{N}=4 $$ SYM theory

“…(B.12) 56 The factor of 2 depends on the convention for the modified effective planar coupling constant (3.19).…”

“…An operator variant of this formulation was given in[17,19] and a different integral representation can be found in[56].…”

Hagedorn Temperature of AdS5/CFT4 via Integrability

“…The partition function and Hagedorn temperature have also been studied in integrable deformations of N ¼ 4 SYM theory up to one-loop order [38], where it was found that although ZðTÞ is different, T H is unchanged. It would be interesting to see whether this statement continues to hold at higher loop orders.…”