Abstract:
We describe the most general treatment of all anomalies both for chiral and massless Dirac fermions, in two-dimensional gravity. It is shown that for this purpose two regularization dependent parameters are present in the effective action. Analogy to the \sc\ model is displayed corresponding to a specific choice of the second parameter, thus showing that the gravitational model contains \a\ relations having no analogy in the \sc\ model.

Abstract:
A metal ring removed from a soap-water solution encloses a film of soap which can be mathematically described as a minimal surface having the ring as its only boundary. This is known to everybody. In this letter we suggest a relativistic extension of the above fluidodynamic system where the soap film is replaced by a Kalb-Ramond gauge potential $\b(x)$ and the ring by a closed string. The interaction between the $\b$-field and the string current excites a new configuration of the system consisting of a relativistic membrane bounded by the string. We call such a classical solution of the equation of motion an axionic membrane. As a dynamical system, the axionic membrane admits a Hamilton-Jacobi formulation which is an extension of the H-J theory of electromagnetic strings.

Abstract:
In this paper we show that a relativistic membrane admits an equivalent representation in terms of the Kalb-Ramond gauge field $F_{\mu\nu\rho}=\partial_{\,[\,\mu}B_{\nu\rho]}$ encountered in string theory. By `` equivalence '' we mean the following: if $x=X(\xi)$ is a solution of the classical equations of motion derived from the Dirac-Nambu-Goto action, then it is always possible to find a differential form of {\it rank three}, satisfying Maxwell-type equations. The converse proposition is also true. In the first part of the paper, we show that a relativistic membrane, regarded as a mechanical system, admits a Hamilton-Jacobi formulation in which the H-J function describing a family of classical membrane histories is given by $\displaystyle{F=dB=dS^1\wedge dS^2\wedge dS^3}$. In the second part of the paper, we introduce a {\it new} lagrangian of the Kalb-Ramond type which provides a {\it first order} formulation for both open and closed membranes. Finally, for completeness, we show that such a correspondence can be established in the very general case of a p-brane coupled to gravity in a spacetime of arbitrary dimensionality.

Abstract:
We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac--Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the $SL(2,R)$ vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the group of residual symmetry in the light--cone gauge.

Abstract:
In this paper we discuss the interplay among (~super-~)coordinate, Weyl and \l\ anomaly both in chiral and non-chiral super-gravity represented by $(1,0)$ and $(1,1)$ two-dimensional models. It is shown that for this purpose two regularization dependent parameters are needed in the effective action. We discuss in {\it full generality} the regularization ambiguities of the induced effective action and recover the corresponding general form of the anomalous Ward Identities. Finally, we explain the difference between chiral and non-chiral super-gravity models in terms of the free parameters and establish relation between these two models by projecting $(1,1)$ into $(1,0)$ super-symmetry.

Abstract:
We construct explicit form of the anomalous effective action, in arbitrary even dimension, for Abelian vector and axial gauge fields coupled to Dirac fermions. It turns out to be a surprisingly simple extension of 2D Schwinger model effective action.

Abstract:
In this letter we implement a recently proposed {\it spacetime duality} approach to dualize a two dimensional, Abelian, gauge field theory, which has no dual version under $p$--duality. Our result suggests that spacetime duality spans a new, wider, class of dual theories, which cannot be related one to another by $p$--duality transformations.

Abstract:
We have developed dualization of ordinary and ``Stueckelberg compensated'' massive phase for the Kalb-Ramond theory. The compensated phase allows to study the interplay between spin jumping and duality. We show that spin jumping is caused by mass, while gauge symmetry is not necessary for this effect to take place.

Abstract:
We show that 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode, induces energy level splitting, and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of SU(2) invariance of the noncommutative model.

Abstract:
The idea that a background of invisible material pervades the whole universe is as old as the history of natural philosophy. Modern particle physics and cosmology support that idea and identify in the cosmic vacuum the ultimate source of matter-energy, both seen and unseen, in the universe. In the framework of the inflation-axion scenario, we suggest an unusual realization of the Higgs mechanism which converts the latent energy of the vacuum into observable mass. The existence of a new spontaneously broken symmetry is pointed out which has the same effect of the Peccei-Quinn symmetry in creating axions as pseudo-Goldstone bosons. However such particles are eliminated from the physical spectrum in favor of massive pseudoscalar particles.