We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, S = A/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.
Limits for the applicability of the equivalence principle are considered in the context of low-energy effective field theories. In particular, we find a class of higherderivative interactions for the gravitational and electromagnetic fields which produce dispersive photon propagation. The latter is illustrated by calculating the energydependent contribution to the deflection of light rays.
We study the effect of a momentum ( k ) lattice as a regulator of quantum field theory. An an example, we compute the vacuum polarization in noncompact (linearized) QED from k-lattice perturbation theory to one-loop order and study the continuum limit. The amplitude has a finite part plus logarithmically, linearly, and quadratically divergent terms. The amplitude violates gauge invariance (Ward identity) and Lorentz (Euclidean) invariance and is nonlocal. For example, the linear term -~l k is nonlocal. Renormalization requires nonlocal counterterms, which is not inconsistent because the original action on the k lattice already has a nonlocality. We explicitly give the counterterms, which render the amplitude Lorentz and gauge invariant to recover the standard result. PACS number(s): 11.15.Ha, 12.20.D~
Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.
We present results of a numerical simulation of the 44 model in the symmetric phase close to the critical line, using a momentum lattice and Langevin updating. We discuss how to extract physics from the zero-momentum behavior of the correlation function. As an example, we have computed mR and ZR and compared it with the analytical results of Liischer and Weisz.
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