Probing D0-D6 Black Hole Configuration: 2-Loop Matrix Theory Correction to D0-Brane Effective Action

TL;DR

This paper calculates the 2-loop matrix theory effective action for a D0-brane in a D0-D6 bound state background, revealing uncanceled divergences that highlight the nondecoupling of massive string states.

Contribution

It provides the first direct 2-loop matrix theory calculation for a D0-D6 system, identifying divergences and discussing their physical implications.

Findings

2-loop matrix theory calculation performed for D0-D6 configuration

Uncanceled ultraviolet divergences found in the 2-loop effective action

Results support the nondecoupling of massive open string states from the D6-brane

Abstract

We present a calculation of the matrix theory 2-loop effective action for a D0-brane in the background of the recently discussed D0-D6 bound state configuration. The effective DBI action of a D0-brane probe in the background of the corresponding 4-dimensional non-supersymmetric black hole solution to low-energy type IIA string theory compactified on a 6-torus is known to agree with the matrix theory calculation at 1-loop order, in the limit in which the ratio of the D0-brane to the D6-brane charges carried by the black hole is large. Agreement at 2-loop between the supergravity description and a conjectured nonabelian BDI effective superYang-Mills description has also been recently reported. However, we find uncanceled ultraviolet divergences in our direct matrix theory calculation of the 2-loop effective action. This is consistent with the expected nondecoupling of massive open string states from the 6-brane.