Brane webs and 1/4-BPS geometries

TL;DR

This paper explores the geometries generated by brane webs preserving eight supercharges, establishing consistency conditions, and analyzing specific configurations like (p,q) strings, membranes, and D3 branes, with a focus on regularity and boundary conditions.

Contribution

It derives the supergravity solutions for brane webs, clarifies conditions for consistent configurations, and connects these to probe analysis and boundary conditions for regular geometries.

Findings

(p,q) string solutions are inconsistent unless web segments are straight and charge-oriented.

Membrane and D3 brane geometries require holomorphic profiles for consistency.

A unique gravity solution exists for any allowed source distribution.

Abstract

We discuss brane webs preserving eight supercharges and derive geometries produced by them. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to be in a perfect agreement with results of the probe analysis. In particular, solutions of IIB SUGRA describing (p,q) stings are inconsistent, unless the web consists of straight line segments whose orientation is correlated with charges of the string. The geometries produced by membranes and D3 branes are only consistent if brane profiles are holomorphic. Using perturbation theory, we show that a unique gravity solution exists for any allowed distribution of sources. We also revisit 1/4-BPS geometries with AdS_p x S^q asymptotics and derive the boundary conditions leading to regular geometries. All degenerate limits of regular solutions are shown to agree with expectations from the brane probe analysis.