Supergravity description of field theories on curved manifolds and a no go theorem

TL;DR

This paper constructs supergravity solutions for branes on curved manifolds, explores their low-energy limits, and establishes a no-go theorem for certain non-singular compactifications in gravity theories.

Contribution

It provides new supergravity solutions for branes on Riemann surfaces and proves a no-go theorem for non-singular Randall-Sundrum and de-Sitter compactifications.

Findings

Found supersymmetric M-theory compactifications to AdS_5.

Proposed a criterion for permissible singularities in supergravity.

Proved no non-singular Randall-Sundrum or de-Sitter compactifications for broad gravity classes.

Abstract

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form $R^d \times \Sigma$ where $\Sigma$ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside $K3$ or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to $AdS_5$. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.