R4 corrections to conifolds and G2-holonomy spaces

Abstract Motivated by examples that appeared in the context of string theory—gauge theory duality, we consider corrections to supergravity backgrounds induced by higher derivative ( R 4 +⋯) terms in superstring effective action. We argue that supersymmetric solutions that solve BPS conditions at the leading (supergravity) order continue to satisfy a 1st order “RG-type” system of equations with extra source terms encoding string (or M-theory) corrections. We illustrate this explicitly on the examples of R 4 corrections to generalized resolved and deformed 6d conifolds and a class of non-compact 7d spaces with G 2 holonomy. Both types of backgrounds get non-trivial modifications which we study in detail, stressing analogies between the two cases.