Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensions

We investigate the matching of eigenvalue densities of Wilson loops in SU(N) lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions are nearly identical when the traces of the loops are equal. We show that the matching is present to at least second order in the strong-coupling expansion, and also to second order in perturbation theory. We find that in the continuum limit there is matching at all values of the trace for bare Wilson loops. We confirm numerically that there is matching in these limits and find there are small violations away from them. We discuss the implications for the bulk transitions and for non-analytic gap formation at N = infinity in 2+1 and 3+1 dimensions.Comment: 23 pages, 10 figure

Polarization from the oscillating magnetized accretion torus

We study oscillations of accretion torus with azimuthal magnetic field. For several lowest-order modes we calculate eigenfrequencies and eigenfunctions and calculate corresponding intensity and polarization light curves using advanced ray-tracing methods.Comment: 5 pages, 3 figures, Proceedings of the conference "The coming of age of X-ray polarimetry", Rome, Italy, 27-30 April 200

A simple approach towards the sign problem using path optimisation

We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a one-dimensional Bose gas with chemical potential. We identify the main contribution to the sign problem in this case as coming from a nearest neighbour interaction and approximately cancel it by an explicit deformation of the integration contour. We extend the obtained expressions to more general ones, depending on a small set of parameters. We find the optimal values of these parameters on a small lattice and study their range of validity. We also identify precursors for the onset of the sign problem. A fast method of evaluating the Jacobian related to the contour deformation is proposed and its numerical stability is examined. For a particular choice of lattice parameters, we find that our approach increases the lattice size at which the sign problem becomes serious from $L \approx 32$ to $L \approx 700$. The efficient evaluation of the Jacobian ($O(L)$ for a sweep) results in running times that are of the order of a few minutes on a standard laptop.Comment: V1: 25 pages, 8 figures; V2: 28 pages, 8 figures, the methods used for finding the contour parameters are clarified, further discussion added, typos corrected, refs adde

Lattice String Field Theory: The linear dilaton in one dimension

We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in the particularly simple case of a one-dimensional linear dilaton and analyse the results.Comment: V1: 74 pages, 35 figures. V2: 75 pages, 35 figures, refs added, typos corrected, some clarification