Fuzzy Cosets and their Gravity Duals

TL;DR

This paper explores how changing background fields in string theory can produce various fuzzy coset geometries from D-branes and examines their gravity duals, revealing multi-centered solutions with brane singularities.

Contribution

It introduces new fuzzy coset configurations derived from D-branes in different RR-form backgrounds and analyzes their gravity duals in a leading order approximation.

Findings

Constructed fuzzy cosets S^2 x S^2, CP^2, and SU(3)/(U(1) x U(1)).

Identified multi-centered gravity solutions with brane singularities.

Discussed dipole and quadrupole moments in these configurations.

Abstract

Dp-branes placed in a certain external RR (p+4)-form field expand into a transverse fuzzy two-sphere, as shown by Myers. We find that by changing the (p+4)-form background other fuzzy cosets can be obtained. Three new examples, S^2 X S^2, CP^2 and SU(3)/(U(1) X U(1)) are constructed. The first two are four-dimensional while the last is six-dimensional. The dipole and quadrupole moments which result in these configurations are discussed. Finally, the gravity backgrounds dual to these vacua are examined in a leading order approximation. These are multi-centered solutions containing (p+4)- or (p+6)-dimensional brane singularities.