D. V. Vassilevich

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with

Graviton 1-loop partition function for 3-dimensional massive gravity

2+1

Parity-odd effects and polarization rotation in graphene

-dimensional fermions interacting with

Space-time noncommutativity tends to create bound states

3+1

Generalised massive gravity one-loop partition function and AdS/(L)CFT

-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

Global and local aspects of spectral actions

Thegraviton1-loop partition function in Euclidean topologically massivegravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.

Enhanced Casimir effect for doped graphene

We show that the presence of parity-odd terms in the conductivity (i.e. in the polarization tensor of Dirac quasiparticles in graphene) leads to the rotation of polarization of the electromagnetic waves passing through suspended samples of graphene. Parity-odd Chern–Simons-type contributions appear in external magnetic fields, giving rise to a quantum Faraday effect (though other sources of parity-odd effects may also be discussed). The estimated order of the effect is well above the sensitivity limits of modern optical instruments.

Duality symmetry of the p-form effective action and supertrace of the twisted de Rham complex

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.

THE FADDEEV-POPOV TRICK IN THE PRESENCE OF BOUNDARIES

The graviton 1-loop partition function is calculated for Euclidean generalised massive gravity (GMG) using AdS heat kernel techniques. We find that the results fit perfectly into the AdS/(L)CFT picture. Conformal Chern-Simons gravity, a singular limit of GMG, leads to an additional contribution in the 1-loop determinant from the conformal ghost. We show that this contribution has a nice interpretation on the conformal field theory side in terms of a semi-classical null vector at level two descending from a primary with conformal weights (3/2, −1/2).

Induced classical gravity

The principal object in noncommutative geometry is the spectral triple consisting of an algebra , a Hilbert space and a Dirac operator . Field theories are incorporated in this approach by the spectral action principle, which sets the field theory action to , where f is a real function such that the trace exists and ? is a cutoff scale. In the low-energy (weak-field) limit, the spectral action reproduces reasonably well the known physics including the standard model. However, not much is known about the spectral action beyond the low-energy approximation. In this paper, after an extensive introduction to spectral triples and spectral actions, we study various expansions of the spectral actions (exemplified by the heat kernel). We derive the convergence criteria. For a commutative spectral triple, we compute the heat kernel on the torus up to the second order in gauge connection and consider limiting cases.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker?s 75th birthday devoted to ?Applications of zeta functions and other spectral functions in mathematics and physics?.