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D. V. Vassilevich

Publications and source records attributed to D. V. Vassilevich.

At least 55 records · Page 3Linked to original sources
arXiv2005

Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.

hep-th↗
arXiv2004

Nonsmooth backgrounds in quantum field theory

The one-loop renormalization in field theories can be formulated in terms of the heat kernel expansion. In this paper we calculate leading contributions of discontinuities of background fields and their derivatives to the heat kernel coefficients. These results are then used to estimate contributions of the discontinuities to the Casimir energy. Sign of such contribution is defined solely by the order of discontinuous derivative. We also discuss renormalization in the presence of singular (delta-function) potentials. We show that an independent surface tension counterterm is necessary. This observation seems to resolve some contradictions in previous calculations.

hep-th↗
arXiv2004

Non-commutative heat kernel

We consider a natural generalisation of the Laplace type operators for the case of non-commutative (Moyal star) product. We demonstrate existence of a power law asymptotic expansion for the heat kernel of such operators on T^n. First four coefficients of this expansion are calculated explicitly. We also find an analog of the UV/IR mixing phenomenon when analysing the localised heat kernel.

hep-th↗
arXiv2003

Space-time non-commutativity tends to create bound states

We study the spectrum of fluctuations about static solutions in 1+1 dimensional non-commutative scalar field models. In the case of soliton solutions non-commutativity leads to creation of new bound states. In the case of static singular solutions an infinite tower of bound states is produced whose spectrum has a striking similarity to the spectrum of confined quark states.

hep-th↗
arXiv2003

Heat kernel expansion: user's manual

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).

hep-th↗
arXiv2003

Chiral anomaly for local boundary conditions

It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate boundary contributions to the chiral anomaly for local (bag) boundary conditions. As a by-product some new results on the heat trace asymptotics are also obtained.

hep-th↗
arXiv2003

Positive specific heat of the quantum corrected dilaton black hole

Path integral quantization of dilaton gravity in two dimensions is applied to the CGHS model to the first nontrivial order in matter loops. Our approach is background independent as geometry is integrated out exactly. The result is an effective shift of the Killing norm: the apparent horizon becomes smaller. The Hawking temperature which is constant to leading order receives a quantum correction. As a consequence, the specific heat becomes positive and proportional to the square of the black hole mass.

hep-th↗
arXiv2003

Quantum corrections to the mass of the supersymmetric vortex

We calculate quantum corrections to the mass of the vortex in N=2 supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a box and apply the zeta function regularization. The boundary conditions inevitably violate a part of the supersymmetries. Remaining supersymmetry is however enough to ensure isospectrality of relevant operators in bosonic and fermionic sectors. A non-zero correction to the mass of the vortex comes from finite renormalization of couplings.

hep-th↗
arXiv2003

Virtual Black Holes in Generalized Dilaton Theories (and Their Special Role in String Gravity)

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models, among them spherically reduced theories and the string inspired dilaton black hole (CGHS model). We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way asymptotic states, tree-level vertices and tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the CGHS model all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.

hep-th↗
arXiv2001

Boundary dynamics and multiple reflection expansion for Robin boundary conditions

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)ϕ=0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.

hep-th↗
arXiv2001

S-matrix for s-wave gravitational scattering

In the s-wave approximation the 4D Einstein gravity with scalar fields can be reduced to an effective 2D dilaton gravity coupled nonminimally to the matter fields. We study the leading order (tree level) vertices. The 4-particle matrix element is calculated explicitly. It is interpreted as scattering with formation of a virtual black hole state. As one novel feature we predict the gravitational decay of s-waves.

gr-qc↗
arXiv2001

Spectral branes

We study the objects (called spectral branes or S-branes) which are obtained by imposing non-local spectral boundary conditions at the boundary of the world sheet of the bosonic string. They possess many nice properties which make them an ideal test ground for the string theory methods. Depending on a particular choice of the boundary operator S-branes may be commutative or non-commutative. We demonstrate that projection of the B-field on the brane directions (i.e. on the components which actually influence the boundary conditions) is done with the help of the chirality operator. We show that the T-duality transformation maps an S-brane to another S-brane. At the expense of introducing non-local interactions in the bulk we construct also a duality transformation between S-branes and D-branes or open strings.

hep-th↗
arXiv2000

Hawking radiation and Hawking flux from spherical reduction

Using heat kernel techniques we show that the relation between Hawking temperature and radiation flux known from Einstein gravity in D dimensions can be reproduced from the spherically reduced action. A recent controversy regarding the D=2 anomaly for that case is discussed. The generalized effective Polyakov action in the presence of a dilaton field is presented.

gr-qc↗
arXiv2000

Discrete Symmetries of Functional Determinants

We study discrete (duality) symmetries of functional determinants. An exact transformation of the effective action under the inversion of background fields $β(x) \to β^{-1}(x)$ is found. We show that in many cases this inversion does not change functional determinants. Explicitly studied models include a matrix theory in two dimensions, the dilaton-Maxwell theory in four dimensions on manifolds without a boundary, and a two-dimensional dilaton theory on manifolds with boundaries. Our results provide an exact relation between strong and weak coupling regimes with possible applications to string theory, black hole physics and dimensionally reduced models.

hep-th↗
arXiv2000

Renormalizability of the open string sigma model and emergence of D-branes

Rederiving the one-loop divergences for the most general coupling of the open string sigma model by the heat kernel technique, we distinguish the classical background field from the mean field of the effective action. The latter is arbitrary, i.e. does not fulfil the boundary conditions. As a consequence a new divergent counter term strongly suggests the introduction of another external one-form field (beside the usual gauge field), coupled to the normal derivative at the boundary. Actually such a field has been proposed in the literature for different reasons, but its full impact never seems to have thoroughly investigated before. The beta function for the resulting renormalizable model is calculated and the consequences are discussed, including the ones for the Born-Infeld action. The most exciting property of the new coupling is that it enters the coefficient in front of the normal derivative in Neumann boundary conditions. For certain values of the background fields this coefficient vanishes, leading to Dirichlet boundary conditions. This provides a natural mechanism for the emergence of D-branes.

hep-th↗
arXiv2000

Open strings, Born--Infeld action and the heat kernel

In the derivation of the Born-Infeld action for the case with a nontrivial boundary of the string world sheet the appearance of a new term changes the conformal anomaly. This may have many consequences, especially also in the study of generalized interacting brane systems.

hep-th↗