Exact Renormalization Group for O(4) Gauged Supergravity

We study exact renormalization group (RG) in O(4) gauged supergrav-ity using the effective average action formalism. The nonperturbative RG equations for cosmological and newtonian coupling constants are found. It is shown the existence of (nonstable) fixed point of these equations. The solution of RG equation for newtonian coupling constant is qualitatively the same as in Einstein gravity (i.e. it is growing at large distances). There was recently much activity in the study of nonperturbative RG dynamics in field theory models (for recent refs., see [1]). One of the versions of nonperturbative RG based on the effective average action has been developed in ref. [2] for Einstein gravity (the gauge dependence problem in this formalism has been studied in ref [3]). The nonperturbative RG equations for cosmological and newtonian coupling constants have been obtained in ref. [2]. The comparison between quantum correction to newtonian coupling from nonperturbative RG [2] and from effective field theory technique [4] has been done. It is quite interesting to generalize nonperturbative RG (or evolution equation) to supersymmetric versions of gravity theories. The theories of such type with cosmological term are gauged supergravities (SG), which may show