One loop thermal effective action

We compute the one loop effective action for a Quantum Field Theory at finite temperature, in the presence of background gauge fields, employing the Heat-Kernel (HK) method. This method enables us to compute the thermal corrections to the Wilson coefficients associated with effective operators, which emerge after integrating out heavy scalars and fermions from a generic UV theory at the one loop. The Heat-Kernel coefficients are functions of non-zero background ‘electric’, ‘magnetic’ fields, and Polyakov loops. In this work, we consider the contributions from the loops with heavy propagators only. We provide the model independent local effective Lagrangian up to dimension six without assuming any particular form of UV theory. We highlight the presence of boundary operators which are absent in zero temperature field theory. We discuss the novelty of the HK method that elegantly captures the effects of non-zero background ‘electric’, ‘magnetic’ fields, and Polyakov loops which are mostly overlooked in literature, but may play an important role in related phenomenology. We compute, using our formalism, the Coleman-Weinberg effective potential at finite temperature including the effects the Polyakov loops and higher dimensional operators.