Corrections to scaling in multicomponent polymer solutions

We calculate the correction-to-scaling exponent $\omega_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of $\omega_T$ in a system of interacting self-avoiding walks gives $\omega_T = 0.415(20)$. A field-theory analysis based on five- and six-loop perturbative series leads to $\omega_T = 0.41(4)$. We also verify the renormalization-group predictions for the scaling behavior close to the ideal-mixing point.Comment: 21 page

Twisted K-Theory of Lie Groups

I determine the twisted K-theory of all compact simply connected simple Lie groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze the exceptions noted by Bouwknegt et al.Comment: 16 page

Tunneling and Quantum Noise in 1-D Luttinger Liquids

We study non-equilibrium noise in the transmission current through barriers in 1-D Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or non-equilibrium) contour. The charges tend to reorganize as a dipole gas, which we use to describe the tunneling statistics. Intra-dipole correlations contribute to the high-frequency ``Josephson'' noise, which has an algebraic singularity at $\omega=e^*V/\hbar$, whereas inter-dipole correlations are responsible for the low-frequency noise. Inter-dipole interactions give a $1/t^2$ correlation between the tunneling events that results in a $|\omega|$ singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the $|\omega|$ singularity, but its form should remain $\sim |\omega|$ to all orders in perturbation theory.Comment: RevTex, 9 figures available upon request, cond-mat/yymmnn

Renormalization Ambiguities in Chern-Simons Theory

We introduce a new family of gauge invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In the particular case $s=0$ we get an explicit example of a gauge invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to $k$ is reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1) fermionic effective actions.Comment: 10 pages, harvmac, no changes, 1 Postscript figure (now included

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte

Topics on the geometry of D-brane charges and Ramond-Ramond fields

In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called *-problem and make some brief remarks about it.Comment: 29 pages, no figure

The scaling behaviour of screened polyelectrolytes

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex

Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology, thus providing a method to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. The local cohomology is shown to be related to the cohomology of jet bundles by means of the variational bicomplex theory. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology introduced in [6], we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part