One-loop Quantum Corrections Research Articles

Entropy of the Quantum Electromagnetic Field in Static, Spherically Symmetric Dilaton Black Holes

The quantum correction to the entropy of four-dimensional nonextreme static,spherically symmetric dilaton black holes arising from electromagnetic fields isinvestigated by 't Hooft's “brick wall” model. The Garfinkle-Horowitz-Strominger,Gibbons-Maeda, and Garfinkle-Horne dilaton black holes areconsidered. It is shown that the one-loop quantum correction arising from theelectromagnetic fields is exactly twice that due to a massless scalar field. Theresult agrees with that of the Schwarzschild and Reissner-Nordstrom blackholes.

Quantum corrections to the thermodynamics of charged 2D black holes

We consider one-loop quantum corrections to the thermodynamics of a black hole in generic 2-dimensional dilaton gravity. The classical action is the most general diffeomorphism invariant action in 1+1 space-time dimensions that contains a metric, dilaton, and Abelian gauge field, and having at most second derivatives of the fields. Quantum corrections are introduced by considering the effect of matter fields conformally coupled to the metric and non-minimally coupled to the dilaton. Back reaction of the matter fields (via non-vanishing trace conformal anomaly) leads to quantum corrections to the black hole geometry. Quantum corrections also lead to modifications in the gravitational action and hence in expressions for thermodynamic quantities. One-loop corrections to both geometry and thermodynamics (energy, entropy) are calculated for the generic dilaton theory. This formalism is applied to a charged black hole in spherically symmetric gravity and to a rotating BTZ black hole.

Energy, central charge, and the BPS bound for 1 + 1-dimensional supersymmetric solitons

We consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric θ 4 and sine-Gordon models in 1 + 1 dimensions. In both models, we unambiguously calculate the correction to the energy in a simple renormalization scheme and obtain ΔH = − m/2 π, in agreement with previous results. Furthermore, we show that there is an identical correction to the central charge, so that the BPS bound remains saturated in the one-loop approximation. We extend these results to arbitrary 1 + 1-dimensional supersymmetric theories.

One-loop quantum holography for higher dimensional black holes

The one-loop quantum corrections to the free energy associated with scalar field in a higher dimensional static curved space-time is investigated making use of the conformal transformation method. For a space-time with bifurcate horizon, horizon divergences are accounted for choosing the Planck length as natural cutoff. The leading term in the high temperature quantum correction satisfies holographically the “area law”, like the tree level Bekenstein-Hawking term. Furthermore it is stressed that only for the asymptotically AdS black holes one may have a microscopic interpretation of the entropy also at quantum level.

One-Loop Quantum Corrections to Thermodynamics of Black Holes with Global Monopoles

Quantum corrections are studied for a black holewith a global monopole charge in a 2D model obtained byspherisymmetric reduction of the 4D action. Thebackreaction of the Hawking radiation on the geometry is studied perturbatively for conformal matter.It is shown that the metric and the position of horizonchange by an amount of order ℏ. Within theoff-shell approach the one-loop thermodynamicquantities, energy, and entropy are found. They are shownto contain two parts, one due to the hole itself and oneto the hot gas surrounding it. The deviation of thequantum-corrected entropy from the classical one is given.

Quantum fluctuations of classical Skyrmions in quantum Hall ferromagnets

In this article, we discuss the effect of the zero-point quantum fluctuations to improve the results of the minimal field theory that has been applied to study Skyrmions in the quantum Hall systems. Our calculation, which is based on the semiclassical treatment of the quantum fluctuations, shows that the one-loop quantum correction provides more accurate results for the minimal field theory.

Finite quantum fluctuations about static field configurations

We develop an unambiguous and practical method to calculate one-loop quantum corrections to the energies of classical time-independent field configurations in renormalizable field theories. We show that the standard perturbative renormalization procedure suffices here as well. We apply our method to a simplified model where a charged scalar couples to a neutral "Higgs" field, and compare our results to the derivative expansion.

Graceful exit problem and stress-energy-momentum tensors revisited in the two-dimensional string cosmology

We study the graceful exit problem and the role of the stress-energy-momentum tensors in the two-dimensional string cosmology. The one-loop quantum correction of conformal fields is incorporated in the arbitrary large N limit to ensure exact quantum solvability. The only solution which gives the bounded curvature with the asymptotic flatness is restricted to the first branch under some conditions. However, even in this case, the accelerating expansion is forever. We show that the only nonvanishing quantum stress-momentum tensor is the pressure part ( T xx ) which is of relevance to the dynamical evolution of the universe in the comoving coordinate. The quantum energy part is zero since the negative contribution of the induced conformal matters always cancels the positive quantity of the induced dilaton part in terms of the constraint equations.

Differential regularization of Chern-Simons-Maxwell spinor and scalar electrodynamics

Differential regularization is used to investigate the one-loop quantum corrections to Chern-Simons-Maxwell spinor and scalar electrodynamics. We illustrate the techniques to write the loop amplitudes in coordinate space. The short-distance expansion method is developed to perform the Fourier transformation of the amplitudes into momentum space and the possible renormalization ambiguity in Chern-Simons type gauge theories in terms of differential regularization is discussed. We also stress that the surface terms appearing in the differential regularization should be kept along for finite theories and they will result in the finite renormalization ambiguity.

Quantum solitons at strong coupling

We examine the effect of one-loop quantum corrections on the formation of nontopological solitons in a strongly coupled scalar-fermionic Yukawa theory. The exact one fermion loop contribution is incorporated by using a nonlocal method to correct the local derivative expansion (DE) approximation of the effective action. As the Yukawa coupling is increased we find that the nonlocal corrections play an increasingly important role. The corrections cause the scalar field to increase in depth while maintaining its size. This increases the energy of the bag configuration, but this is compensated for by more tightly bound fermionic states with lower energy. In contrast with the semiclassical picture without quantum corrections, the binding energy is small, and the total energy scales directly with the Yukawa coupling. This confirms the qualitative behavior found in earlier work using the second order DE, although the quantitative solutions differ. {copyright} {ital 1997} {ital The American Physical Society}

Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action and black hole entropy

According to Gibbons and Hawking a consistent variational procedure applied to the gravitational action requires a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in the quantum effective action for the matter non-minimally coupled to metric. It is shown that one has to add a special boundary term to the matter action analogous to the Gibbons-Hawking one. This boundary term modifies the one-loop quantum corrections to give a correct balance for the effective action as well. This means that the boundary UV divergences do not require independent renormalization and are automatically renormalized simultaneously with their volume part. This result is derived for arbitrary non-minimally coupled matter. The example of the 2D Maxwell field is considered in much detail. The relevance of the results obtained to the problem of the renormalization of the black hole entropy is discussed.

Conical geometry and quantum entropy of a charged Kerr black hole.

We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an arbitrary periodization in Euclidean space there exists a conical singularity at the horizon. Its $\delta$-function like curvatures are calculated and are shown to behave similar to the static case. The heat kernel expansion for a scalar field on this conical space background is derived and the (divergent) quantum correction to the entropy is obtained. It is argued that these divergences can be removed by renormalization of couplings in the tree-level gravitational action in a manner similar to that for a static black hole.

One-loop quantum corrections to the thermodynamics of charged black holes.

Quantum corrections are studied for a charged black hole in a two-dimensional (2D) model obtained by spherisymmetric reduction of the 4D Einstein-Maxwell theory. The classical (tree-level) thermodynamics is reformulated in the framework of the off-shell approach, considering systems at arbitrary temperature. This implies a conical singularity at the horizon and modifies the gravitational action by terms defined on the horizon. A consistent variational procedure for the action functional is formulated. It is shown that the free energy reaches an extremum on the regular manifold with $T={T}_{H}$. The one-loop contribution to the action in the Liouville-Polyakov from is reexamined. All the boundary terms are taken into account and the dependence on the state of the quantum field is established. The modification of the Liouville-Polyakov term for a 2D space with a conical defect is derived. The back reaction of the Hawking radiation on the geometry is studied and the quantum-corrected black hole metric is calculated perturbatively. Within the off-shell approach the one-loop thermodynamical quantities, energy, and entropy, are found. They are shown to contain a part due to hot gas surrounding the black hole and a part due to the hole itself. It is noted that the contribution of the hot gas can be eliminated by appropriate choice of the (generally, nonflat) reference geometry. The deviation of the "entropy - horizon area" relation for the quantum-corrected black hole from the classical law is discovered and possible physical consequences are discussed.

Two-dimensional quantum-corrected eternal black hole.

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.

(1+2)-Dimensional model of the early universe

An anisotropic cosmological model is obtained by solving (1+3)-dimensional field equations. The topology of the model isR1 ⊗M2 ⊗S1, whereR1 is the real line (time axis),M2 is 2-dimensional space, andS1 is the circle. Employing the method of Kaluza-Klein type compactification onS1 and one-loop quantum correction to scalar fields, an effective (1+2)-dimensional gravity is obtained. The resulting (1+2)-dimensional cosmological model of the early universe is derived.

THERMODYNAMICS OF BLACK HOLE IN (N+3) DIMENSIONS FROM EUCLIDEAN N-BRANE THEORY

In this letter we consider an N-brane description of an (N+3)-dimensional black hole horizon. First of all, we start by examining in more detail a previous work where a string theory is used in describing the dynamics of the event horizon of a four-dimensional black hole. This is an attempt to understand the black hole thermodynamics by an effective two-dimensional field theory of the event horizon of a black hole. Then we consider a particle model defined on one-dimensional Euclidean line in a three-dimensional black hole as a target spacetime metric. By solving the field equations we find a “worldline instanton” which connects the past event horizon with the future one. This solution gives us the exact value of the Hawking temperature and to leading order the Bekenstein-Hawking formula of black hole entropy. We also show that this formalism is extensible to an arbitrary spacetime dimension. Finally we make a comment of many recent works of one-loop quantum correction to the black hole entropy.

One-loop quantum corrections to the entropy for a four-dimensional eternal black hole

The first quantum corrections to the free energy for an eternal four-dimensional black hole are investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. The quadratic and logarithmic divergences as well as a finite part associated with the first quantum correction to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the internal energy should cancel. Some comments on the divergences of the entropy are also presented.

SOME QUANTUM ASPECTS OF COMPLEX VECTOR FIELDS WITH CHERN-SIMONS TERM

Complex vector fields with Maxwell, Chern-Simons and Proca terms are minimally coupled to an Abelian gauge field. The consistency of the spectrum is analyzed and one-loop quantum corrections to the self-energy are explicitly computed and discussed. The incorporation of two-loop contributions and the behavior of tree level scattering amplitudes in the limit of high center-of-mass energies are commented on.

Higher derivative gravity in two dimensions.

The 2D gravity described by the action which is an arbitrary function of the scalar curvature $f(R)$ is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function $f=R \ln R$ the model coupled with scalar (conformal) matter is exactly integrated and is shown to describe a black hole of the 2D dilaton gravity type. The influence of one-loop quantum corrections on a classical black hole configuration is studied by including the Liouville-Polyakov term. The resulting model turns out to be exactly solvable. The general solution is analyzed and shown to be free from the space-time singularities for a certain number of scalar fields.

Conical singularity and quantum corrections to the entropy of a black hole

For a general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by a regular surface is used to determine the curvature tensors for such a metric. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional (2D) and four-dimensional cases are considered. The entropy of Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe a finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.