String Theory seminar - Elias Kiritsis Seminar

Abstract: We study the F-theorem in the context of field theories on S^3 using gauge-gravity duality, with the radius of S^3 playing the role of a RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR. If the operator perturbing the UV CFT has dimension \Delta > 3/2 these F-functions correspond to an appropriately renormalised free energy. However, if the perturbing operator has dimension \Delta < 3/2 it is the quantum effective potential, i.e., the Legendre transform of the free energy, which gives rise to good F-functions. We check that these observations hold beyond holography for the case of a free fermion on S^3 (\Delta=2) and the free boson on S^3 (\Delta=1), solving the puzzle regarding the non-monotonicity of the free energy for the free boson first observed in 1105.4598. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.