Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary

The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of quantum corrections to the effective action past one-loop necessitates diagramatic techniques. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. In such a context the stated evaluations can be accomplished through a consistent interpretation of the Feynman rules within the spherical formulation of the theory for which the method of images allows. To this effect, the mathematical consequences of such an interpretation are analyzed and the spherical formulation of the Feynman rules on the bounded manifold is, as a result, developed.Comment: 12 pages, references added. To appear in Classical and Quantum Gravit

Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary

The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the theory to second order in the scalar self-coupling pursued herein involves explicit calculations of up to third loop-order and reveals that, in addition to the renormalisation of the scalar self-coupling and scalar field, the removal of all divergences necessitates the introduction of conformally non-invariant counterterms proportional to $R\Phi^2$ and $K\Phi^2$ in the bare scalar action as well as counterterms proportional to $RK^2$, $R^2$ and $RK$ in the gravitational action. The substantial backreaction effects and their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the cut-off $N_0$ and in p.4 regarding the gravitational action. Certain reference-related ommission corrected. To appear in Classical and Quantum Gravit

Visualization of vortex bound states in polarized Fermi gases at unitarity

We analyse theoretically a single vortex in 3D trapped atomic Fermi gases with population polarization near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied for the majority component. As a result, the local density difference at the core center acquires a sudden rise at low temperautres. This provides a visualization of the lowest bound state within the absorption imaging technique. As the polarization increases, the core expands gradually, and correspondingly, the energy of the lowest bound state decreases.Comment: 4 pages, and 4 figures; Published version in PR

On Fermionic T-duality of Sigma modes on AdS backgrounds

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma models on AdS backgrounds. We show that the sigma model on $AdS_5\times S^1$ background is self-dual under fermionic T-duality. We also construct new integrable sigma models on $AdS_2\times CP^n$. These backgrounds could be realized as supercosets of SU supergroups for arbitrary $n$, but could also be realized as supercosets of OSp supergroups for $n=1,3$. We find that the supercosets based on SU supergroups are self-dual under fermionic T-duality, while the supercosets based on OSp supergroups are not. However, the reasons of OSp supercosets being not self-dual under fermionic T-duality are different. For $OSp(6|2)$ case, corresponding to $AdS_2\times CP^3$ background, the failure is due to the singular fermionic quadratic terms, just like $AdS_4\times CP^3$ case. For $OSp(3|2)$ case, the failure is due to the shortage of right number of $\kappa$-symmetry to gauge away the fermionic degrees of freedom, even though the fermionic quadratic term is not singular any more. More general, for the supercosets of the OSp supergroups with superalgebra $B(n,m)$, including $AdS_2\times S^{2n}$ and $AdS_4\times S^{2n}$ backgrounds, the sigma models are not self-dual under fermionic T-duality as well, obstructed by the $\kappa$-symmetry.Comment: 17 pages; Clarfications on kappa symmetries, references added;Published versio

Fingering convection and cloudless models for cool brown dwarf atmospheres

This work aims to improve the current understanding of the atmospheres of brown dwarfs, especially cold ones with spectral type T and Y, whose modeling is a current challenge. Silicate and iron clouds are believed to disappear at the photosphere at the L/T transition, but cloudless models fail to reproduce correctly the spectra of T dwarfs, advocating for the addition of more physics, e.g. other types of clouds or internal energy transport mechanisms. We use a one-dimensional (1D) radiative/convective equilibrium code ATMO to investigate this issue. This code includes both equilibrium and out-of-equilibrium chemistry and solves consistently the PT structure. Included opacity sources are H2-H2, H2-He, H2O, CO, CO2, CH4, NH3, K, Na, and TiO, VO if they are present in the atmosphere. We show that the spectra of Y dwarfs can be accurately reproduced with a cloudless model if vertical mixing and NH3 quenching are taken into account. T dwarf spectra still have some reddening in e.g. J - H compared to cloudless models. This reddening can be reproduced by slightly reducing the temperature gradient in the atmosphere. We propose that this reduction of the stabilizing temperature gradient in these layers, leading to cooler structures, is due to the onset of fingering convection, triggered by the destabilizing impact of condensation of very thin dust.Comment: Accepted in ApJ

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory

In this paper we study the one- and two-loop corrections to the four-point amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity methods we express the one- and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the two-loop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N=4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals.Comment: 32 pages and 6 figures. v2: minus sign corrections, ref updated v3: Published versio

Thermodynamics of the \phi^4 theory in tadpole approximation

Relying on the Luttinger-Ward theorem we derive a thermodynamically selfconsistent and scale independent approximation of the thermodynamic potential for the scalar $\phi^4$ theory in the tadpole approximation. The resulting thermodynamic potential as a function of the temperature is similar to the one of the recently proposed screened perturbation theory.Comment: 6 pages, including 1 eps figur

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction