Background Effects on Thermal Free Energy in Conformal Field Theories

Abstract

We compute background corrections to the thermal free energy of free conformal field theories (CFTs) with a global abelian symmetry defined on a box with all sides infinitely long by turning on a flat gauge field in general dimensions. This result is applied to the U(N) maximally supersymmetric Yang-Mills theory, the ABJ(M) theory, and the free U(N) vector model in four, three, and two spacetime dimensions, respectively. In these examples, the thermal free energies monotonically increase as the background field does, and cross a zero within the valid range. We argue that the systems undergo a phase transition at the zero, where the effective degrees of freedom fall off similarly to the color-confinement one, and that it always occurs if the number of matter fields is greater than a critical value. We comment for this phase transition to circumvent the Mermin-Wagner-Coleman theorem in two spacetime dimensions.