The global phase diagram of a modular invariant two dimensional statistical model

A generalization of the Coulomb Gas model with modular SL(2, Z)-symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2,Z) acting on the two-dimensional parameter space gives us a nested shape of its global phase diagram and all the infrared stable fixed points. Finally we propose a connection with the 2-dimensional Conformal Field Theory description of the Fractional Quantum Hall Effect.Comment: 17 pages LaTeX + 1 figur

Constraints on discrete symmetries from anomaly cancellation in compactified superstring theories

Compactified string theories give rise to discrete symmetries which are essential if they are to provide a realistic low energy theory. We find that in a class of four dimensional string theories these symmetries are constrained by similar conditions to those discrete anomaly cancellation conditions found in the case the discrete symmetry is a residue of a spontaneously broken gauge symmetry. Such conditions strongly constrain the allowed form of the low energy effective theory.Comment: 8 pages, OUTP-93-14

Radiative corrections to the Casimir force and effective field theories

Radiative corrections to the Casimir force between two parallel plates are considered in both scalar field theory of one massless and one massive field and in QED. Full calculations are contrasted with calculations based on employing ``boundary-free'' effective field theories. The difference between two previous results on QED radiative corrections to the Casimir force between two parallel plates is clarified and the low-energy effective field theory for the Casimir effect in QED is constructed.Comment: 17 pages, revte

RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR

Temperature inversion symmetry in the Casimir effect with an antiperiodic boundary condition

We present explicitly another example of a temperature inversion symmetry in the Casimir effect for a nonsymmetric boundary condition. We also give an interpretation for our result.Comment: 4 page

Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions

A model consisting of a single massless scalar field with a topological coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z) symmetry as a consequence of the gauge invariance. We propose that by adding impurities the model can be used to describe transitions between Quantum Hall plateaux. This leads to a correlation length exponent of 20/9, in excellent agreement with the most recent experimental measurements.Comment: 25 pages, minor changes in data discussion, Section V on connection with staircase model is expanded References added. Interpretive comments added in section 3 about the critical condition. with improved terminolog

A Vector Non-abelian Chern-Simons Duality

Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the pure non-abelian Chern-Simons action at the classical level. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.Comment: 14+1 pages, LaTeX file, no figures, version to appear in Phys. Rev

Topological oscillations of the magnetoconductance in disordered GaAs layers

Oscillatory variations of the diagonal ($G_{xx}$) and Hall ($G_{xy}$) magnetoconductances are discussed in view of topological scaling effects giving rise to the quantum Hall effect. They occur in a field range without oscillations of the density of states due to Landau quantization, and are, therefore, totally different from the Shubnikov-de Haas oscillations. Such oscillations are experimentally observed in disordered GaAs layers in the extreme quantum limit of applied magnetic field with a good description by the unified scaling theory of the integer and fractional quantum Hall effect.Comment: 4 pages, 4 figure

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde