Thermodynamic properties of thin films of superfluid 3He-A

The pairing correlations in superfluid He-3 are strongly modified by quasiparticle scattering off a surface or an interface. We present theoretical results and predictions for the order parameter, the quasiparticle excitation spectrum and the free energy for thin films of superfluid He-3. Both specular and diffuse scattering by a substrate are considered, while the free surface is assumed to be a perfectly reflecting specular boundary. The results are based on self-consistent calculations of the order parameter and quasiparticle excitation spectrum at zero pressure. We obtain new results for the phase diagram, free energy, entropy and specific heat of thin films of superfluid He-3.Comment: Replaced with an updated versio

SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop

SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability.Comment: 46 pages, version to appear in Comput.Phys.Com

D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops

The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.Comment: 31 pages, revtex, 12 figure

Correlation functions in the non-relativistic AdS/CFT correspondence

We study the correlation functions of scalar operators in the theory defined as the holographic dual of the Schroedinger background with dynamical exponent z=2 at zero temperature and zero chemical potential. We offer a closed expression of the correlation functions at tree level in terms of Fourier transforms of the corresponding n-point functions computed from pure AdS in the lightcone frame. At the loop level this mapping does not hold and one has to use the full Schroedinger background, after proper regularization. We explicitly compute the 3-point function comparing it with the specific 3-point function of the non-relativistic theory of cold atoms at unitarity. We find agreement of both 3-point functions, including the part not fixed by the symmetry, up to an overall normalization constant.Comment: 32 pages, 7 figures; v2: typos corrected, references added and additional discussion about the case of compact number-direction, includes new appendix with the computations of the 2 and 3 point function for the compact number-direction case. The general results remain the same. Version published in Phys.Rev.