The shape of nonabelian D-branes

TL;DR

This paper investigates the bulk energy, charge distributions, and shapes of nonabelian D-branes using supergravity formulas, revealing how noncommutative scalar fields form expected brane geometries in the large N limit.

Contribution

It provides a detailed analysis of the bulk structures and shapes of nonabelian D-branes, including the effects of noncommutative scalar fields and the resolution of distribution ambiguities.

Findings

Energy distributions confirm force balance in string-brane networks.

Fuzzy D-brane charge distributions approach expected shapes at large N.

Finite N distributions pose interpretational challenges, addressed by ordering ambiguities.

Abstract

We evaluate bulk distribution of energies, pressures and various D-brane/F-string charges generated by nontrivial matrix configurations in nonabelian D-brane effective field theories, using supergravity source density formulas derived originally in Matrix theory. Off-diagonal elements of worldvolume nonabelian fields, especially transverse scalar fields, induce various interesting bulk structures exhibiting the shape of branes. First, we study the energy distribution of string-brane networks generated in the bulk by the Yang-Mills monopoles and the 1/4 BPS dyons, and confirm force balance of them. An application to the Yang-Mills description of recombination of intersecting D-branes gives results indicating presence of the tachyon matter. Second, we analyse the shape of fuzzy D-branes given by nonabelian scalar fields which are mutually noncommutative. We employ fuzzy S^2, fuzzy S^4 and fuzzy cylinder/supertube as matrix configurations of N D0-branes representing higher dimensional noncommutative D-branes. We find that in the continuum (large N) limit the D-brane charge distributions become in the expected shape of a sphere or a cylinder with an infinitesimal thickness. However, the distributions found for finite N are difficult to interpret, which leaves a puzzle for a possible dual description in terms of higher dimensional D-branes. A resolution is provided with use of an ordering ambiguity in the charge density formulas.