D0 Matrix Mechanics: New Fuzzy Solutions at Large N

TL;DR

This paper explores new fuzzy geometries like the fuzzy cylinder and plane in a large N matrix model related to D-brane physics, revealing novel solutions and bound states.

Contribution

It introduces new classes of solutions in the large N limit of a D-brane matrix model, including fuzzy cylinder and plane geometries, extending previous finite N results.

Findings

Discovered fuzzy cylinder and plane solutions at large N.

Identified a warped fuzzy plane solution.

Demonstrated these solutions as D0-branes forming D2 bound states.

Abstract

We wish to consider in this report the large N limit of a particular matrix model introduced by Myers describing D-brane physics in the presence of an RR flux background. At finite N, fuzzy spheres appear naturally as non-trivial solutions to this matrix model and have been extensively studied. In this report, we wish to demonstrate several new classes of solutions which appear in the large N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a warped fuzzy plane. The latter two solutions arise from a possible "central extension" to our model that arises after we account for non-trivial issues involved in the large N limit. As is the case for finite N, these new solutions are to be interpreted as constituent D0-branes forming D2 bound states describing new fuzzy geometries.