International Journal of Modern Physics A

The status of the project is described: the activity on long term characterization of water optical and oceanographic parameters at the Capo Passero site candidate for the Mediterranean km³ neutrino telescope; the feasibility study; the physics performances and underwater technology for the km³; the activity on NEMO Phase 1, a technological demonstrator that has been deployed at 2000 m depth 25 km offshore Catania; the realization of an underwater infrastructure at 3500 m depth at the candidate site (NEMO Phase 2).

We demonstrate that the two (1+1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, constitute an algebra that is reminiscent of the algebra obeyed by the de Rham cohomological operators. The topological features of the above theory are discussed in terms of the BRST and co-BRST operators. The super-de Rham cohomological operators are exploited in the derivation of the nilpotent (anti-)BRST, (anti-)co-BRST symmetry transformations and the equations of motion for all the fields of the theory, within the framework of the superfield formulation. The derivation of the equations of motion, by exploiting the super-Laplacian operator, is a completely new result in the framework of the superfield approach to BRST formalism. In an Appendix, the interacting 2D Abelian gauge theory (where there is a coupling between the U(1) gauge field and the Dirac fields) is also shown to provide a tractable field theoretical model for the Hodge theory.

We present a method for computing the nonperturbative mass-gap in the theory of bosonic membranes in flat background space–times. The analysis is extended to the study of membranes coupled to background fluxes as well. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a "hidden" parameter, which turns out to be being the related to the dimensionality of the background space. We then proceed to develop a large N perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large N perturbation theory is then translated into the language of quantum spin chains and the one-loop spectra of various bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space–times. The spin chains corresponding to the large N effective Hamiltonians for the relevant matrix models are generically not integrable. However, we are able to find large integrable subsectors for all the spin chains of interest. Moreover, the continuum limits of the spin chains are mapped to integrable Landau–Lifschitz models even if the underlying spin chains are not integrable. Apart from membranes in flat space–times, the recently proposed matrix models (arXiv:hep-th/0607005) for noncritical membranes in plane wave type space–times are also analyzed within the paradigm of quantum spin chains. The bosonic sectors of all the models proposed in arXiv:hep-th/0607005 are diagonalized at the one-loop level and an intriguing connection between the existence of supersymmetric vacua and one-loop integrability is also presented.

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

It has recently been shown that a Hagedorn phase of string gas cosmology may provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. A distinctive signature of this structure formation scenario would be a slight blue tilt of the spectrum of gravitational waves. In this paper we give more details of the computations leading to these results, and the assumptions underlying them.

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra sphere and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a sphere in two simple cases are obtained.

The quantum properties of localized finite energy solutions to classical Euler–Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant g is constructed, taking into account the conservation laws of momentum and angular momentum (invariance of the action with respect to the group of motion M(3) of three-dimensional Euclidean space) rigorously in every order of perturbation theory.

The standard electroweak model with Dirac neutrinos is extended by way of the principles of electroweak quark–lepton symmetry and weak topological-charge confinement to account for quark–lepton charge relations which, if not accidental, are indicative of charge structures. A mixing in quarks and leptons of underlying integer local charges with integer weak topological charges associated with an additive group Z₃, fixed by the anomaly cancellation requirement, is discussed. It is found that the electroweak difference between topological quarks and leptons is the nonequivalence between the topological vacua of their weak field configurations, produced by a four-instanton which carries the topological charge, induces the universal fractional piece of charge distinguishing quarks from leptons, and breaks the underlying symmetry. The constituent quarks of the standard model appear as coming from topological quarks, via the weak four-instanton event. Dual transitions occur for leptons. It is shown that several other fundamental problems left open in the standard electroweak model with Dirac neutrinos are solved: the one-to-one correspondence between quark and lepton flavors, the existence of three generations, the conservation and ungauging of B-L, the electric charge quantization, and the confinement of fractional electric charges.