Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

Renormalisation of the Nonperturbative Thermal Pressure

We show how the fully resummed thermal pressure is rendered ultraviolet finite by standard zero-temperature renormalisation. The analysis is developed in a 6-dimensional scalar model that mimics QED and has $N$ flavours. The $N\to\infty$ limit of the model can be calculated completely. At a critical temperature, one of the degrees of freedom has vanishing screening mass like the transverse gauge bosons in four-dimensional finite-temperature perturbation theory. The renormalised nonperturbative interaction pressure of this model is evaluated numerically.Comment: 27 pages, plain tex, with 10 figures embedded using eps

Comparative Planetary Atmospheres: Models of TrES-1 and HD209458b

We present new self-consistent atmosphere models for transiting planets TrES-1 and HD209458b. The planets were recently observed with the Spitzer Space Telescope in bands centered on 4.5 and 8.0 $\mu$m, for TrES-1, and 24 $\mu$m, for HD209458b. We find that standard solar metallicity models fit the observations for HD209458b. For TrES-1, which has an T_eff ~300 K cooler, we find that models with a metallicity 3-5 times enhanced over solar abundances can match the 1$\sigma$ error bar at 4.5 $\mu$m and 2$\sigma$ at 8.0$\mu$m. Models with solar abundances that included energy deposition into the stratosphere give fluxes that fall within the 2$\sigma$ error bars in both bands. The best-fit models for both planets assume that reradiation of absorbed stellar flux occurs over the entire planet. For all models of both planets we predict planet/star flux ratios in other Spitzer bandpasses.Comment: Accepted to the Astrophysical Journal Letters, May 17, 200

Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering

We study the nonrelativistic limit of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. The renormalization of the relativistic model, in the Coulomb gauge, is discussed. We employ a procedure to calculate scattering amplitudes for low momenta that generates their $|p|/m$ expansion and separates the contributions coming from high and low energy intermediary states. The two body scattering amplitude is calculated up to order $p^2/m^2$. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle scattering amplitude reduces to the Aharonov-Bohm one is a strictly nonrelativistic feature. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering. A nonrelativistic reduction scheme and an effective nonrelativistic Lagrangian to account for the relativistic corrections are proposed.Comment: 22 pages, 8 figures, revtex, to be published in Int. J. Mod. Phys.

The dual of Janus -:- an interface CFT

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, =0, and this is confirmed in first order in the discontinuity.Comment: 24 pages, 1 figure; references adde

Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions

We consider N=1 supersymmetric gauge theories in which the couplings are allowed to be space-time dependent functions. Both the gauge and the superpotential couplings become chiral superfields. As has recently been shown, a new topological anomaly appears in models with space-time dependent gauge coupling. Here we show how this anomaly may be used to derive the NSVZ beta function in a particular, well-determined renormalisation scheme, both without and with chiral matter. Moreover we extend the topological anomaly analysis to theories coupled to a classical curved superspace background, and use it to derive an all-order expression for the central charge c, the coefficient of the Weyl tensor squared contribution to the conformal anomaly. We also comment on the implications of our results for the central charge a expected to be of relevance for a four-dimensional C-theorem.Comment: 28 pages, LaTeX, no figure

Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin J=1 are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin J=0.Comment: 30 pages, 3 figures, RevTeX, epsf and psfig style files require

CFT/CFT interpolating RG flows and the holographic c-function

We consider holographic RG flows which interpolate between non-trivial ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the ``superpotentials'' which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic $c$-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the $c$-function in terms of the associated Jost functions. We propose two explicit models that realize UV-IR flows. In the first example we consider a thin wall separating two AdS spaces with different radii, while in the second one the UV region is replaced with an asymptotically AdS space. We find that the holographic $c$-function obeys the expected properties. In particular it reduces to the correct -- nonzero -- central charge in the IR limit.Comment: 20 pages, discussion at the end of sec. 3 and sec. 4.1 change

Star product and the general Leigh-Strassler deformation

We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two Z_3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh-Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of N=4 SYM is preserved, in both beta- (one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the deformation for each amplitude can be extracted in a prefactor. We also conclude that the obtained amplitudes should follow the iterative structure of MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A added, v4: clarification in section 3.