Correspondence principle in quantum gravity

The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that this approach fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the correspondence principle is given directly in terms of the effective action. Gauge independence of the \hbar^0 part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed. Application to the black holes is discussed.Comment: Talk presented at the international meeting "Quantum Gravity and Spectral Geometry", Naples, July 2001. 4 pages, 1 figur

Two-Dimensional Chiral Matrix Models and String Theories

We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a set of coupling constants associated to worldsheet ramification points of various orders. Our approach is closely related to, but simpler than, the string theory describing two-dimensional Yang-Mills theory. Using recently developed character expansion methods we exactly solve the models for target space lattices of arbitrary internal connectivity and topology.Comment: 12 pages, 1 figure, TeX, harvmac.tex, epsf.tex, minor correction

Two-Matrix model with ABAB interaction

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitean matrices A and B with the action S={1\over 2}(\tr A^2+\tr B^2)-{\alpha\over 4}(\tr A^4+\tr B^4) -{\beta\over 2} \tr(AB)^2. This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c=1 coupled to 2D quantum gravity.Comment: harvmac, 24 pages, 5 figures (1 color figure

Analytical treatment of 2D steady flames anchored in high-velocity streams

The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role in determining flame structure. In particular, it is necessary in formulating boundary conditions near the flame anchor, and for the proper account of the flame propagation law. Using the on-shell description of steady anchored flames, a consistent solution of the problem is given. Equations for the flame front position and gas-velocity at the front are obtained. It is demonstrated that they reduce to a second-order differential equation for the front position. Numerical solutions of the derived equations are found.Comment: 15 pages, 6 figure

Renormalization Properties of Softly Broken SUSY Gauge Theories

In the present review we show that renormalizations in a softly broken SUSY gauge theory are not independent but directly follow from those of an unbroken or rigid theory. This is a consequence of a treatment of a softly broken theory as a rigid one in external spurion superfield. This enables one to get the singular part of effective action in a broken theory from a rigid one by a simple modification of the couplings. Substituting the modified couplings into renormalization constants, RG equations, solutions to these equations, approximate solutions, fixed points, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion over the Grassmannian variables. Some examples including the MSSM in low and high $\tan\beta$ regime, SUSY GUTs and the N=2 Seiberg-Witten model are considered.Comment: LaTeX, 25pp, 2 eps figures. Talk at "Continuous Advances in QCD 2002/Arkadyfest

Large-N quantum gauge theories in two dimensions

The partition function of a two-dimensional quantum gauge theory in the large-$N$ limit is expressed as the functional integral over some scalar field. The large-$N$ saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus $g>0$. The existence of a non-trivial saddle point is closely related to the weak coupling behavior of the theory. Possible applications of the method to higher dimensions are briefly discussed.Comment: 6pp., Latex, TAUP-2012-92 (revised: few changes, some references added

Exploring Softly Broken SUSY Theories via Grassmannian Taylor Expansion

We demonstrate that soft SUSY breaking introduced via replacement of the couplings of a rigid theory by spurion superfields has far reaching consequences. Substituting these modified couplings into renormalization constants, RG equations, solutions to these equations, fixed points, finiteness conditions, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion over the Grassmannian variables. This way one can get new solutions of the RG equations. Some examples including the MSSM, SUSY GUTs and the N=2 Seiberg-Witten model are given.Comment: Latex, 10pp, no figure