Holographic Wilsonian renormalization and chiral phase transitions

We explore the role of a holographic Wilsonian cutoff in simple probe brane models with chiral symmetry breaking/restoration phase transitions. The Wilsonian cutoff allows us to define supergravity solutions for off-shell configurations and hence to define a potential for the chiral condensate. We pay particular attention to the need for configurations whose action we are comparing to have the same IR and UV boundary conditions. We exhibit new first- and second-order phase transitions with changing cutoff. We derive the effective potential for the condensate including mean-field and Berezinskii-Kosterlitz-Thouless type continuous transitions.