Comments on Black Holes in Matrix Theory

The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes black strings stretched across the longitudinal direction, near the transition where black strings become unstable to the formation of black holes. It is argued that the appropriate dynamics on the other (black hole) side of the transition is that of the zero modes of the corresponding super Yang-Mills theory. A suggestive mean field theory argument is given for the entropy of black holes in all dimensions. Consequences of the analysis for matrix theory and the holographic principle are discussed.Comment: 15 pages, harvmac, minor errors correcte

Hermitian D-brane solutions

A low-energy background field solution describing D-membrane configurations is constructed which is distinguished by the appearance of a Hermitian metric on the internal space. This metric is composed of a number of independent harmonic functions on the transverse space. Thus this construction generalizes the usual harmonic superposition rule. The BPS bound of these solutions is shown to be saturated indicating that they are supersymmetric. By means of T-duality, we construct more solutions of the IIA and IIB theories.Comment: 14 pages, Latex, no figure

Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thric

Localized Branes and Black Holes

We address the delocalization of low dimensional D-branes and NS-branes when they are a part of a higher dimensional BPS black brane, and the homogeneity of the resulting horizon. We show that the effective delocalization of such branes is a classical effect that occurs when localized branes are brought together. Thus, the fact that the few known solutions with inhomogeneous horizons are highly singular need not indicate a singularity of generic D- and NS-brane states. Rather, these singular solutions are likely to be unphysical as they cannot be constructed from localized branes which are brought together from a finite separation.Comment: 13 pages, RevTex, no figures, few references and comments adde

Statistical Effects and the Black Hole/D-brane Correspondence

The horizon area and curvature of three-charge BPS black strings are studied in the D-brane ensemble for the stationary black string. The charge distributions along the string are used to translate the classical expressions for the horizon area and curvature of BPS black strings with waves into operators on the D-brane Hilbert space. Despite the fact that any `wavy' black string has smaller horizon area and divergent curvature, the typical values of the horizon area and effects of the horizon curvature in the D-brane ensemble deviate negligibly from those of the original stationary black string in the limit of large integer charges. Whether this holds in general will depend on certain properties of the quantum bound states.Comment: 13 pages, RevTex, small errors corrected, some interpretation changed in light of new result

The Nielsen Identities for the Two-Point Functions of QED and QCD

We consider the Nielsen identities for the two-point functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon self-energy and ghost propagator in terms of the gauge dependence of other, independent Green functions.Comment: 25 pages, plain TeX, 4 figures available upon request, MZ-TH/94-0

Can the effective string see higher partial waves?

The semi-classical cross-sections for arbitrary partial waves of ordinary scalars to fall into certain five-dimensional black holes have a form that seems capable of explanation in terms of the effective string model. The kinematics of these processes is analyzed in detail on the effective string and is shown to reproduce the correct functional form of the semi-classical cross-sections. But it is necessary to choose a peculiar value of the effective string tension to obtain the correct scaling properties. Furthermore, the assumptions of locality and statistics combine to forbid the effective string from absorbing more than a finite number of partial waves. The relation of this limitation to cosmic censorship is discussed.Comment: 19 pages, uses harvmac, version to appear in Phys. Rev.

The Perturbative Pole Mass in QCD

It is widely believed that the pole mass of a quark is infrared-finite and gauge-independent to all orders in perturbation theory. This seems not to have been proved in the literature. A proof is provided here.Comment: 12 pages REVTeX with 2 figures; archiving published version with note and references added. If you thought this was proven long ago see http://www-theory.fnal.gov/people/ask/TeX/mPole