Searcharxiv⌕ Search

arXiv subjects

S. Naftulin

Publications and source records attributed to S. Naftulin.

11 recordsLinked to original sources
arXiv1996

The Gross-Neveu model on a sphere with a magnetic monopole

We study, for the first time, the phase structure of the Gross--Neveu model with a combination of a (constant) gravitational and a magnetic field. This has been made possible by our finding of an exact solution to the problem, namely the effective potential for the composite fermions. Then, from the corresponding implicit equation the phase diagram for the dynamical fermion mass is calculated numerically for some values of the magnetic field. %(what can be done with arbitrary precision). For a small magnetic field the phase diagram hints to the possibility of a second order phase transition at some critical curvature. With growing magnetic field only the phase with broken chiral symmetry survives, because the magnetic field prevents the decay of the chiral condensate. This result is bound to have important consequences in early universe cosmology.

hep-th↗
arXiv1995

On higher-derivative dilatonic gravity in two dimensions

We discuss lowering the order of the two-dimensional scalar-tensor $R^2$ quantum gravity, by mapping the most general version of the model to a multi-dilaton gravity, which is essentially the sigma-model coupled with Jackiw-Teitelboim-like gravity. In the continuation of our previous research, we calculate the divergent part of the one-loop effective action in a 2D scalar-tensor (dilatonic) gravity with Ra2-term, which belongs to a specific degenerate case and cannot be obtained from the general expression. The corresponding finiteness conditions are found.

hep-th↗
arXiv1995

On Black Holes in the Theory of Dilatonic Gravity Coupled to a Scalar Field

Taking advantage of the representation of dilatonic gravity with the $R^2$-term under the form of low-derivative dilatonic gravity coupled to an additional scalar, we construct a general renormalizable model motivated by this theory. Exact black hole solutions are found for some special versions of the model, and their thermodynamical properties are described in detail. In particular, their horizons and temperatures are calculated. Finally, the corresponding one-loop effective action is obtained in the conformal gauge, and a number of its properties -including the construction of one-loop finite models-are briefly described.

hep-th↗
arXiv1995

Quantum reparametrizations in the two-dimensional gravity: a look from 2+$ε$ dimensions

We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations. Some of them are shown to be equivalent to the introduction of $2+ε$-dimensional terms into the initially 2-dimensional theory. We also argue that the $β$-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.

hep-th↗
arXiv1994

Quantum reparametrizations in the two-dimensional gravity: a look from 2+$epsilon$ dimensions

We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations.Some of them are shown to be equivalent to the introduction of 2+$epsilon$-dimensional terms into the initially 2-dimensional theory. We also argue that the beta-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.

hep-th↗
arXiv1993

One-Loop Renormalization of Higher-Derivative 2D Dilaton Gravity

A theory of higher-derivative 2D dilaton gravity which has its roots in the massive higher-spin mode dynamics of string theory is suggested. The divergences of the effective action to one-loop are calculated, both in the covariant and in the conformal gauge. Some technical problems which appear in the calculations are discussed. An interpretation of the theory as a particular D=2 higher-derivative $σ$-model is given. For a specific case of higher-derivative 2D dilaton gravity, which is one loop multiplicatively renormalizable, static configurations corresponding to black holes are shown to exist.

hep-th↗
arXiv1993

Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter

Two dimensional dilaton gravity interacting with a four-fermion model and scalars is investigated, all the coefficients of the Lagrangian being arbitrary functions of the dilaton field. The one-loop covariant effective action for 2D dilaton gravity with Majorana spinors (including the four-fermion interaction) is obtained, and the technical problems which appear in an attempt at generalizing such calculations to the case of the most general four-fermion model described by Dirac fermions are discussed. A solution to these problems is found, based on its reduction to the Majorana spinor case. The general covariant effective action for 2D dilaton gravity with the four-fermion model described by Dirac spinors is given. The one-loop renormalization of dilaton gravity with Majorana spinors is carried out and the specific conditions for multiplicative renormalizability are found. A comparison with the same theory but with a classical gravitational field is done.

hep-th↗
arXiv1993

The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities

The one-loop effective action corresponding the general model of dilaton gravity given by the Lagrangian $L=-\sqrt{g} \left[ \frac{1}{2}Z(Φ) g^{μν} \partial_μΦ\partial_νΦ+ C(Φ) R + V (Φ)\right]$, where $Z(Φ)$, $ C(Φ)$ and $V (Φ)$ are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples it is shown that classically equivalent quantum gravities are also perturbatively equivalent at the quantum level, but only on-shell. The renormalization group equations for the generalized effective couplings $Z(Φ)$, $ C(Φ)$ and $V (Φ)$ are written. An analysis of the equations shows, in particular, that the Callan-Giddings-Harvey-Strominger model is not a fixed point of these equations.

hep-th↗
arXiv1993

Convenient Versus Unique Effective Action Formalism in 2D Dilaton-Maxwell Quantum Gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $Ω$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.

hep-th↗
arXiv1992

One Loop Counterterms in 2D Dilaton-Maxwell Quantum Gravity

The renormalization structure of two-dimensional quantum gravity is investigated, in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account, thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.

hep-th↗