New Brane Solutions from Killing Spinor Equations

TL;DR

This paper constructs new supersymmetric brane solutions in supergravity by replacing parts of known solutions with Ricci flat and Einstein manifolds, including novel singular Ricci flat manifolds, expanding the landscape of supergravity compactifications.

Contribution

It introduces a method to generate new brane solutions using Killing spinor relations, including singular Ricci flat manifolds, and explores their supersymmetry properties and compactifications.

Findings

New supersymmetric brane solutions in D=11 and D=10 supergravity.

Construction of singular Ricci flat manifolds as cones over U(1) bundles.

Asymptotic solutions approaching these singular vacua.

Abstract

In a recent paper, we have pointed out a relation between the Killing spinor and Einstein equations. Using this relation, new brane solutions of D=11 and D=10 type IIB supergravity theories are constructed. It is shown that in a brane solution, the flat world-volume directions, the smeared transverse directions and the sphere located at a fixed radial distance can be replaced with any Lorentzian Ricci flat, Euclidean Ricci flat and Einstein manifolds, respectively. The solution obtained in this fashion is supersymmetric when the Ricci flat and Einstein manifolds have Killing spinors. We generalize intersecting brane solutions, in which M5, M2 and D3-branes also wrap over the cycles determined by the K\"{a}hler forms of Ricci flat K\"{a}hler manifolds. New, singular, Ricci flat manifolds as (generalized) cones over the U(1) bundles over Ricci flat K\"{a}hler spaces are constructed. These manifolds have covariantly constant spinors and give rise to new, supersymmetric, Ricci flat compactifications of non-gauged supergravity theories. We find M2 and D3-brane solutions, which asymptotically approach these singular vacua.