Quantum corrections to the noncommutative kink

We calculate quantum corrections to the mass of noncommutative phi^4 kink in (1+1) dimensions for intermediate and large values of the noncommutativity parameter theta. All one-loop divergences are removed by a mass renormalization (which is different from the one required in the topologically trivial sector). For large theta quantum corrections to the mass grow linearly with theta signaling about possible break down of the perturbative expansion.Comment: 18 pages, v2: minor change

Quantum aspects of a noncommutative supersymmetric kink

We consider quantum corrections to a kink of noncommutative supersymmetric phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of time derivatives in the action, we are able to define supercharges and a Hamiltonian by using an unconventional canonical formalism. We calculate the quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of fluctuations) which coincides with its' value in corresponding commutative theory independently of the noncommutativity parameter. The renormalization also proceeds precisely as in the commutative case. The vacuum expectation value of the new Hamiltonian is also calculated and appears to be consistent with the value of the quantum energy E of the kink.Comment: 20 pages, v2: a reference adde

Induced Gauge Theory on a Noncommutative Space

We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.Comment: Typos corrected, one reference added; eqn. (49) corrected, one equation number added; 30 page

Heat Trace Asymptotics on Noncommutative Spaces

This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered

Heat kernel and number theory on NC-torus

The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC $\phi^4$ theory on \T^4, we show that this theory can be made renormalizable at least at one loop, and may be even beyond

Casimir force between Chern-Simons surfaces

We calculate the Casimir force between two parallel plates if the boundary conditions for the photons are modified due to presence of the Chern-Simons term. We show that this effect should be measurable within the present experimental technique.Comment: 8 pages, 1 figur

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.Comment: Latex, 18 pp; v2 reference added; v3 minor change

Relativistic Gauge Conditions in Quantum Cosmology

This paper studies the quantization of the electromagnetic field on a flat Euclidean background with boundaries. One-loop scaling factors are evaluated for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of Faddeev-Popov quantum amplitudes is performed by using zeta-function regularization, and is compared with the space-time covariant evaluation of the same amplitudes. It is shown that a particular gauge condition exists for which the corresponding operator matrix acting on gauge modes is in diagonal form from the beginning. Moreover, various relativistic gauge conditions are studied in detail, to investigate the gauge invariance of the perturbative quantum theory.Comment: 26 pages, plain TeX, no figure

Spectral action for torsion with and without boundaries

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter $\theta$ of the boundary conditions, and show that $\theta=0$ is a critical point of the action in any dimension and at all orders of the expansion.Comment: 16 pages, references adde

One-Loop Amplitudes in Euclidean Quantum Gravity

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.Comment: 26 pages, plain TeX, no figure