Duality in deformed coset fermionic models

We study the $SU(2)_k/U(1)$-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the $Z_k$ parafermion theory are constructed as gauge invariant composites. We find that the theory presents a duality symmetry that interchanges the roles of the spin and dual spin operators. For two particular values of the coupling constant we find that the theory recovers conformal invariance and the gauge symmetry is enlarged. We also find a novel self-dual point.Comment: 13 pages, LaTex. Minor corrections. One reference added. Version to appear in Nuc. Phys.

Genetic diversity of common toads (Bufo bufo) along the Norwegian coast : disjunct distribution of locally dominant haplotypes

Little is known about the phylogeographic history of amphibian populations along the western Fennoscandinavian coast. In the present study, we focus on the common toad (Bufo bufo) and document the spatial distribution of mitochondrial DNA (cytb) haplotypes at 20 localities along its coastal Norwegian range. Two common haplotypes (out of eight haplotypes in total) were represented by 142 out of the 154 (92%) investigated individuals. However, they were shared at only three localities and clustered at two separate geographic regions each. The most common haplotype (55% of individuals) has previously been found to be abundant across central and eastern Europe, whereas the second most common haplotype (37% of individuals) has so far only been recorded in Sweden. The disjunct distribution of genetic lineages is in line with an assumption that the Norwegian coastline was postglacially colonised both from the south as well as across mountain passes from the east. Our data support previous studies on the phylogeography of Fennoscandinavia that revealed that post-glacial recolonisation patterns led to a pronounced spatial structure of local populations

Universal aspects of string propagation on curved backgrounds

String propagation on D-dimensional curved backgrounds with Lorentzian signature is formulated as a geometrical problem of embedding surfaces. When the spatial part of the background corresponds to a general WZW model for a compact group, the classical dynamics of the physical degrees of freedom is governed by the coset conformal field theory SO(D-1)/SO(D-2), which is universal irrespective of the particular WZW model. The same holds for string propagation on D-dimensional flat space. The integration of the corresponding Gauss-Codazzi equations requires the introduction of (non-Abelian) parafermions in differential geometry.Comment: 15 pages, latex. Typo in Eq. (2.12) is corrected. Version to be published in Phys. Rev.

The Abelian Higgs Model as an Ensemble of Vortex Loops

In the London limit of the Ginzburg-Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation- and translation invariant measure of integration over their shapes leads to effective sine-Gordon theories of the dual fields. The representations of the partition functions of both grand canonical ensembles are derived in the form of the integrals over the vortex dipoles and the small vortex loops, respectively. By virtue of these representations, the bilocal correlator of the vortex dipoles (loops) is calculated in the low-energy limit. It is further demonstrated that once the vortex dipoles (loops) are considered as such an ensemble rather than individual ones, the London limit of the Ginzburg-Landau theory (Abelian Higgs model) with external monopoles is equivalent up to the leading order in the inverse UV cutoff to the compact QED in the corresponding dimension with the charge of Cooper pairs changed due to the Debye screening.Comment: 17 pages, LaTeX2e, no figures, dedicated to Prof. Yu.A. Simonov on the occasion of his 65-th birthday, final published version (minor corrections, references added

ADE functional dilogarithm identities and integrable models

We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization Group flow of 2D integrable, ADE-related quantum field theories. The known sum rules for the central charge of critical fixed points can be obtained as special cases of these. We conjecture that similar functional identities can be constructed for any rational integrable quantum field theory with factorized S-matrix and support it with extensive numerical checks.Comment: LaTeX, 9 pages, no figure

Equilibrium Two-Dimensional Dilatonic Spacetimes

We study two-dimensional dilaton gravity coupled to massless scalar fields for static solutions. In addition to the well known black hole, we find another class of solutions that may be understood as that of the black hole in equilibrium with a radiation bath. We claim that there is a solution that is qualitatively unchanged after including Hawking radiation and back-reaction and is furthermore geodesically complete. We compute the thermodynamics of these spacetimes and their mass. We end with a brief discussion of the linear response about these solutions, its significance to stability and noise and a speculation regarding the endpoint of Hawking evaporation in four dimensions. (plain TeX; one figure, available upon request.)Comment: 22 pages, M.I.T. preprint CTP#217

The two-boundary sine-Gordon model

We study in this paper the ground state energy of a free bosonic theory on a finite interval of length $R$ with either a pair of sine-Gordon type or a pair of Kondo type interactions at each boundary. This problem has potential applications in condensed matter (current through superconductor-Luttinger liquid-superconductor junctions) as well as in open string theory (tachyon condensation). While the application of Bethe ansatz techniques to this problem is in principle well known, considerable technical difficulties are encountered. These difficulties arise mainly from the way the bare couplings are encoded in the reflection matrices, and require complex analytic continuations, which we carry out in detail in a few cases.Comment: 34 pages (revtex), 8 figure

Fermion Condensates of massless QED2QED_2 at Finite Density in non-trivial Topological Sectors

Vacuum expectation values of products of local bilinears $\bar\psi\psi$ are computed in massless $QED_2$ at finite density. It is shown that chiral condensates exhibit an oscillatory inhomogeneous behaviour depending on the chemical potential. The use of a path-integral approach clarifies the connection of this phenomenon with the topological structure of the theory.Comment: 16 pages, no figures, To be published in Phys.Rev.

A formulation of the Yang-Mills theory as a deformation of a topological field theory based on background field method and quark confinement problem

By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically non-trivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.Comment: 45 pages, 3 figures included in LaTe

Massive Spin 3/2 Electrodynamics

We study the general non-minimally coupled charged massive spin 3/2 model both for its low energy phenomenological properties and for its unitarity, causality and degrees of freedom behaviour. When the model is viewed as an effective theory, its parameters (after ensuring the correct excitation count) are related to physical characteristics, such as the magnetic moment g factor, by means of low energy theorems. We also provide the corresponding higher spin generalisation. Separately, we consider both low and high energy unitarity, as well as the causality aspects of our models. None (including truncated N=2 supergravity) is free of the minimal model's acausality.Comment: 23 pages, 1 figure, LaTeX and axodraw.sty, novel Majorana-type term included; results unaltere