Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories

We show that generic three-dimensional $\mathcal N=2$ quiver super Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.Comment: V1, 5 pages; V2, 13 pages, circular Wilson loops added, published versio

Wilson function transforms related to Racah coefficients

The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explicit expressions for the Racah coefficients. The Racah coefficients are Wilson polynomials and Wilson functions. This leads to natural interpretations of the Wilson function transforms. As an application several sum and integral identities are obtained involving Wilson polynomials and Wilson functions. We also compute Racah coefficients for U_q(\su(1,1)), which turn out to be Askey-Wilson functions and Askey-Wilson polynomials.Comment: 48 page

The Static Potential to O(\alpha^2) in Lattice Perturbation Theory

We present a calculation of Wilson loops, and the static inter-quark potential to $O(\alpha^2)$ in lattice perturbation theory. This is carried out with the Wilson, Symanzik-Weisz, and Iwasaki gauge actions and the Wilson, Sheikholeslami-Wohlert, and Kogut-Susskind dynamical fermion action for small Wilson loops, and with the Wilson gauge action and each of the dynamical quark actions in the case of the static potential.Comment: Lattice2001(improvement) 3 pages, 3 figure

Chiral perturbation theory for lattice QCD including O(a^2)

The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD with Wilson fermions are constructed. The results are generalized to partially quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory with Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 3 pages, Lattice2003 (spectrum

Loop Equation and Wilson line Correlators in Non-commutative Gauge Theories

We investigate Schwinger-Dyson equations for correlators of Wilson line operators in non-commutative gauge theories. We point out that, unlike what happens for closed Wilson loops, the joining term survives in the planar equations. This fact may be used to relate the correlator of an arbitrary number of Wilson lines eventually to a set of {\it closed} Wilson loops, obtained by joining the individual Wilson lines together by a series of well-defined cutting and joining manipulations. For closed loops, we find that the non-planar contributions do not have a smooth limit in the limit of vanishing non-commutativity and hence the equations do not reduce to their commutative counterparts. We use the Schwinger-Dyson equations to derive loop equations for the correlators of Wilson observables. In the planar limit, this gives us a {\it new} loop equation which relates the correlators of Wilson lines to the expectation values of closed Wilson loops. We discuss perturbative verification of the loop equation for the 2-point function in some detail. We also suggest a possible connection between Wilson line based on an arbitrary contour and the string field of closed string.Comment: typos corrected and references updated; version to appear in Nucl. Phys.

Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory

We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.Comment: 40 pages, 12 figure

An expansion formula for the Askey-Wilson function

The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion formula at hand, the image under the Askey-Wilson function transform of an Askey-Wilson polynomial multiplied by an analogue of the Gaussian is computed explicitly. As a special case of these formulas a q-analogue (in one variable) of the Macdonald-Mehta integral is obtained, for which also two alternative, direct proofs are presented.Comment: 24 pages. Some remarks added in section 6 on the connection with moment problem