Sergei D. Odintsov

Renormalization-group improved effective Lagrangian for interacting theories in curved spacetime

Abstract A method for finding the renormalization group (RG) improved effective Lagrangian for a massive interacting field theory in curved spacetime is presented. As a particular example, the λϕ4-theory is considered and the RG improved effective. Lagrangian is explicitly found up to second order in the curvature tensors. As a further application, the curvature-induced phase transitions are discussed for both the massive and the massless versions of the theory. The problems which appear when calculating the RG improved effective Lagrangian for gauge theories are discussed, taking as example the asymptotically free SU(2) gauge model.

Phase structure of renormalizable four-fermion models in spacetimes of constant curvature.

A number of 2D and 3D four-fermion models which are renormalizable, in the 1/{ital N} expansion, in a maximally symmetric constant curvature space are investigated. To this purpose, a powerful method for the exact study of spinor heat kernels and propagators on maximally symmetric spaces is reviewed. The renormalized effective potential is found for any value of the curvature and its asymptotic expansion is given explicitly, both for small and for strong curvature. The influence of gravity on the dynamical symmetry-breaking pattern of some U(2) flavorlike and discrete symmetries is described in detail. The phase diagram in {ital S}{sup 2} is constructed and it is shown that, for any value of the coupling constant, a curvature exists above which chiral symmetry is restored. For the case of {ital H}{sup 2}, chiral symmetry is always broken. In three dimensions, in the case of positive curvature, {ital S}{sup 3}, it is seen that curvature can induce a second-order phase transition. For {ital H}{sup 3} the configuration given by the auxiliary fields equated to zero is not a solution of the gap equation. The physical relevance of the results is discussed. {copyright} {ital 1996 The American Physical Society.}

Improved effective potential in curved spacetime and quantum matter–higher derivative gravity theory

We develop a general formalism to study the renormalization-group- (RG-)improved effective potential for renormalizable gauge theories, including matter-

Chiral symmetry breaking in d = 3 NJL model in external gravitational and magnetic fields

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GUT's in curved spacetime: Running gravitational constants, Newtonian potential, and the quantum-corrected gravitational equations.

-gravity, in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easily obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase transitions) are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. The stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the standard model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.

A four-dimensional theory for quantum gravity with conformal and non-conformal explicit solutions

The phase structure of the {ital d}=3 Nambu{endash}Jona-Lasinio model in curved spacetime with a magnetic field is investigated in leading order of the 1/{ital N} expansion and in the linear curvature approximation (an external magnetic field is treated exactly). The possibility of chiral symmetry breaking under the combined action of the external gravitational and magnetic fields is shown explicitly. In some circumstances the chiral symmetry may be restored due to the compensation of the magnetic field by the gravitational field. {copyright} {ital 1996 The American Physical Society.}

Asymptotic regimes in quantum gravity at large distances and running Newtonian and cosmological constants

The running coupling constants (in particular, the gravitational one) are studied in asymptotically free GUTs and in finite GUTs in curved spacetime, with explicit examples. The running gravitational coupling is used to calculate the leading quantum GUT corrections to the Newtonian potential, which turn out to be of logarithmic form in asymptotically free GUTs. A comparison with the effective theory for the conformal factor —where leading quantum corrections to the Newtonian potential are again logarithmic— is made. A totally asymptotically free O(N) GUT with quantum higher derivative gravity is then constructed, using the technique of introducing renormalization group (RG) potentials in the space of couplings. RG equations for the cosmological and gravitational couplings in this theory are derived, and solved numerically, showing the influence of higher-derivative quantum gravity on the Newtonian potential. The RG-improved effective gravitational Lagrangian for asymptotically free massive GUTs is calculated in the strong (almost constant) curvature regime, and the non-singular De Sitter solution to the quantum corrected gravitational equations is subsequently discussed. Finally, possible extensions of the results here obtained are briefly outlined.

One-loop renormalization and asymptotic behaviour of a higher-derivative scalar theory in curved spacetime

The most general version of a renormalizable d=4 theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains 12 independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three non-conformal solutions, given by remarkably simple (albeit non-trivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization-group flows is discussed as well as possible physical applications.

Chiral symmetry breaking in the Nambu-Jona-Lasinio model in curved spacetime with a nontrivial topology.

We consider a multiplicatively renormalizable higher-derivative scalar theory which is used as an effective theory for quantum gravity at large distances (infrared phase of quantum gravity). The asymptotic regimes (in particular, the asymptotically free infrared regime) for the coupling constants---specifically the Newtonian and the cosmological constant---are obtained. The running of the Newton and cosmological constants in the infrared asymptotically free regime may be relevant for solving the cosmological constant problem and for estimating the leading-log corrections to the static gravitational potential.

Effective potential for a covariantly constant gauge field in curved spacetime

Abstract A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations corresponding to two different, multiplicatively renormalizable variants of the same are derived. The analysis of their asymptotic solutions shows that, depending on the sign of one of the coupling constants, we can construct an asymptotically free theory which is also asymptotically conformal invariant at strong (or small) curvature. The connection that can be established between one of the multiplicatively renormalizable variants of the theory and the effective theory of the conformal factor, aiming at the description of quantum gravity at large distances, is investigated.