Probing D0-D6 black hole configuration: Two-loop matrix theory correction to the D0-brane effective action

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 con figuration. The effective DBI action of a D0-brane probe in the background of the corresponding four-dimensional non-supersymmetric black hole solutio n to low-energy type IIA string theory compactified on a 6-torus is known t o 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 bla ck hole is large. Agreement at two loops between the supergravity descripti on and a conjectured non-abelian BDI effective superYang-Mills description has also been recently reported. However, we find uncanceled ultraviolet di vergences in our direct matrix theory calculation of the 2-loop effective a ction. This is consistent with the expected non-decoupling of massive open string states from the 6-brane. (C) 1999 Elsevier Science B.V. All rights r eserved.