The Backreacted K\"ahler Geometry of Wrapped Branes

TL;DR

This paper investigates the geometry of wrapped D3 and M2 branes, revealing how their internal spaces are described by backreacted K"ahler geometries satisfying specific equations, and provides explicit solutions consistent with supersymmetry.

Contribution

It reformulates wrapped brane solutions in canonical form, identifies the associated backreacted K"ahler geometries, and constructs a new class of solutions satisfying Killing spinor equations.

Findings

Explicit form of backreacted K"ahler geometries for wrapped branes

New solutions satisfying supersymmetry conditions

Reformulation of solutions in canonical form

Abstract

For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is known that the internal space is expressible as U(1) fibration over K\"ahler space which satisfies a specific partial differential equation involving the Ricci tensor. In this paper we study the wrapped brane solutions of D3 and M2-branes which were originally constructed using gauged supergravity and uplifted to D=10 and D=11. We rewrite the solutions in canonical form, identify the backreacted K\"ahler geometry, and present a class of solutions which satisfy the Killing spinor equation.