Matrix Model for membrane and dynamics of D-Particles in a curved space-time geometry and presence of form fields

TL;DR

This paper develops a matrix model for membranes in curved space-time with form fields, analyzing D-particle dynamics, polarization effects, and fuzzy solutions like spheres and hyperboloids.

Contribution

It introduces a matrix regularisation for membranes in curved backgrounds with 3-form fields and explores D-particle polarization and fuzzy geometries.

Findings

Riemann curvature induces D-particle polarization

Fuzzy sphere, hyperbolic, and ellipsoid solutions are constructed

Matrix regularisation captures membrane dynamics in complex backgrounds

Abstract

We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we then study the dynamics of D-particles. We show how the Riemann curvature of the target space-time geometry, or any other form fields can polarise the D-Particles, cause entanglement among them and create fuzzy solutions. We review the fuzzy sphere and we present fuzzy hyperbolic and ellipsoid solutions.