  The interplay between electron-electron interactions and weak localization
(or anti-localization) phenomena in two-dimensional systems can significantly
enhance the superconducting transition temperature. We develop the theory of
quantum fluctuations within such multifractally-enhanced superconducting states
in thin films. In conditions of weak disorder, we employ the Finkel'stein
nonlinear sigma model to derive an effective action for the superconducting
order parameter and the quasiclassical Green's function, meticulously
accounting for the influence of quantum fluctuations. This effective action,
applicable for interactions of any strength, reveals the critical role of
well-known collective modes in a dirty superconductor, and its saddle point
analysis leads to modified Usadel and gap equations. These equations
comprehensively incorporate the renormalizations stemming from the interplay
between interactions and disorder, resulting in the non-trivial energy
dependence of the gap function. Notably, our analysis establishes a direct
relation between the self-consistent gap equation at the superconducting
transition temperature and the known renormalization group equations for
interaction parameters in the normal state.
