The electrostatic view on M-theory LLM geometries

TL;DR

This paper reformulates certain M-theory geometries using electrostatic variables, analyzing both regular and singular solutions, and computes their masses consistent with microscopic interpretations.

Contribution

It introduces an electrostatic framework for describing M-theory LLM geometries, including boundary conditions for smooth and singular configurations.

Findings

Identified boundary conditions for regular and singular geometries.

Computed masses of configurations at finite radius, matching microscopic expectations.

Provided a unified electrostatic description of M-theory vacua.

Abstract

We describe the geometry of the R x SO(3) x SO(6) x U(1) invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS_4 x S^7 and AdS_7 x S^4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvature.