R^4 corrections to conifolds and G_2 holonomy metrics

TL;DR

This paper investigates how higher derivative R^4 corrections affect supergravity backgrounds with conifold and G_2 holonomy, showing that supersymmetric solutions persist with modified equations.

Contribution

It demonstrates that supersymmetric solutions at leading order remain valid under R^4 corrections, with explicit examples on conifolds and G_2 spaces illustrating the modifications.

Findings

Supersymmetric solutions satisfy modified first-order equations with source terms.

R^4 corrections induce non-trivial modifications to conifold and G_2 backgrounds.

Analogies between conifold and G_2 cases are highlighted.

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 1-st 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 the generalized resolved and deformed 6-d conifolds and to a class of non-compact 7-d spaces with G_2 holonomy. Both types of backgrounds get non-trivial modifications which we study in detail, stressing analogies between the two cases.