Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background

Abstract

We study one-loop effective action of Berkooz-Douglas Matrix theory and obtain nonabelian action of D0-branes in the background field produced by longitudinal 5-branes. Since these 5-branes do not have D0-brane charge and are not present in BFSS Matrix theory, our analysis can be regarded as an independent test for the coupling of D-branes to general weak backgrounds proposed by Taylor and Van Raamsdonk, and also as a check of consistency between the two versions of Matrix theory. The coupling to the 5-branes which we obtain is basically consistent with the previous proposal, but we point out subtleties in the ordering of matrices for the multipole moments. *

Supersymmetric action of multiple D0-branes from matrix theory

“…( 3.2) below. The first two terms of (3.1) are the ones obtained in the previous paper [16]. We calculate…”

“…We treat the vertices as an expansion around a reference time τ and obtain the effective action as a double expansion in the number of vertices and the number of derivatives, following the procedure described in ref. [16]. Explicit form of the two-fermion (two L) terms of the effective action is given as ‡…”

“…Note that we have defined the complex combination of X m by (φ 1 , φ 2 ) = (X 1 + iX 2 , X 3 + iX 4 ), and that the fermions are expressed as 6D Weyl spinors, which have 4 complex components. As in the previous paper [16], we do not use the SU(2) Majorana convention, for we prefer unconstrained fermions for the loop calculations. The subscripts on the spinors θ + , θ − denote the positive and negative 6D chiralities, respectively (γθ ± = ±θ ± , where γ = γ 0 γ 1 .…”

“…Berkooz-Douglas(BD) Matrix theory is defined by the 0-4 string and 0-0 string sectors of the SYM describing D0-D4 system. In a previous paper [16], we performed one-loop integration of 0-4 fields and obtained the bosonic part of the non-abelian action of D0-branes. We found that the action consists of the terms given from the general proposal of Taylor and Van Raamsdonk by substituting the L5-brane backgrounds, plus the corrections involving extra commutators.…”

“…In this paper, extending the analysis of ref. [16], we calculate the one-loop effective action of BD Matrix theory and obtain non-abelian effective action of D0-branes including the part containing fermionic fields. Especially, we reveal the consequence of the supersymmetry of the classical action.…”