Normal Bundles, Pfaffians and Anomalies

We deal with the problem of diffeomorphism anomaly in theories with branes. In particular we thoroughly analyze the problem of the residual chiral anomaly of a five-brane immersed in M-theory, paying attention to its global formulation in the five-brane world-volume. We conclude that the anomaly can be canceled by a {\it local} counterterm in the five-brane world-volume.Comment: 17 pages, Latex, sign convention changed, typos correcte

Abelian 3-form gauge theory: superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow Region, Russi

Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry

We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c=1 CFT. In this paper we show that p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three dimensional hyperbolic geometry.Comment: 12 pages, no figure

Opening the Pandora's box of quantum spinor fields

Lounesto's classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.Comment: 18 page

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ

Axial gravity: a non-perturbative approach to split anomalies

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue.Comment: 43 pages, some additions in section 6.3 and 6.5 plus minor correction

Bi-photon propagation control with optimized wavefront by means of Adaptive Optics

We present an efficient method to control the spatial modes of entangled photons produced through SPDC process. Bi-photon beam propagation is controlled by a deformable mirror, that shapes a 404nm CW diode laser pump interacting with a nonlinear BBO type-I crystal. Thanks to adaptive optical system, the propagation of 808nm SPDC light produced is optimized over a distance of 2m. The whole system optimization is carried out by a feedback between deformable mirror action and entangled photon coincidence counts. We also demonstrated the improvement of the two-photon coupling into single mode fibers