Functional renormalization group equations for antisymmetric tensor field models at finite temperature

Within the framework of the functional renormalization group, we derived the flow equations for the scale-dependent effective action at finite temperature for models involving an antisymmetric rank-2 tensor field. The analysis focuses on scenarios where the vacuum expectation value emerges due to symmetry breaking patterns, specifically $SU(n) \to USp(n)$ and $SO(n) \to SU(n/2)$. The derived equations provide insights into the behavior of these models under varying scales and temperatures, contributing to the understanding of phase transitions in systems with complex symmetry structures.