Supersymmetric Open Wilson Lines

In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.Comment: 26 pages, 3 figure

An exact formula for the radiation of a moving quark in N=4 super Yang Mills

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in N=4 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.Comment: 22 pages, 5 figures. v2: references added, typos correcte

BPS Wilson Loops on S^2 at Higher Loops

We consider supersymmetric Wilson loops of the variety constructed by Drukker, Giombi, Ricci, and Trancanelli, whose spatial contours lie on a two-sphere. Working to second order in the 't Hooft coupling in planar N=4 Supersymmetric Yang-Mills Theory (SYM), we compute the vacuum expectation value of a wavy-latitude and of a loop composed of two longitudes. We evaluate the resulting integrals numerically and find that the results are consistent with the zero-instanton sector calculation of Wilson loops in 2-d Yang-Mills on S^2 performed by Bassetto and Griguolo. We also consider the connected correlator of two distinct latitudes to third order in the 't Hooft coupling in planar N=4 SYM. We compare the result in the limit where the latitudes become coincident to a perturbative calculation in 2-d Yang-Mills on S^2 using a light-cone Wu-Mandelstam-Leibbrandt prescription. We are not able to calculate the SYM result at the required order in the separation between the latitudes necessary for a match with 2-d Yang-Mills; the result, however, does not preclude such a match.Comment: 39 pages, 15 figures. v2 references added, minor cosmetic changes. v3 minor error in eq. (40) corrected. v4 error in coincident limit of correlator corrected; claims of disagreement with 2-d Yang-Mills retracte

Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio

Defect multiplets of N=1 supersymmetry in 4d

Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called $\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the $\mathcal{S}$-multiplet receives contributions localised on the defect, which indicate the breaking of some translation symmetry and consequently also some supersymmetries. We call this the defect multiplet. We classify such terms corresponding to half-BPS defects which can be either three-dimensional, preserving 3d $\mathcal{N}=1$, or two-dimensional, preserving $\mathcal{N}=(0,2)$. The new terms localised on the defect furnish multiplets of the reduced symmetry and give rise to the displacement operator

Impure Aspects of Supersymmetric Wilson Loops

We study a general class of supersymmetric Wilson loops operator in N = 4 super Yang-Mills theory, obtained as orbits of conformal transformations. These loops are the natural generalization of the familiar circular Wilson-Maldacena operator and their supersymmetric properties are encoded into a Killing spinor that is not pure. We present a systematic analysis of their scalar couplings and of the preserved supercharges, modulo the action of the global symmetry group, both in the compact and in the non-compact case. The quantum behavior of their expectation value is also addressed, in the simplest case of the Lissajous contours: explicit computations at weak-coupling, through Feynman diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence, suggest the possibility of an exact evaluation.Comment: 40 pages, 4 figure

On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze

Wilson loops are calculated within the AdS/CFT correspondence by finding a classical solution to the string equations of motion in AdS_5 x S^5 and evaluating its action. An important fact is that this sigma-model used to evaluate the Wilson loops is integrable, a feature that has gained relevance through the study of spinning strings carrying large quantum numbers and spin-chains. We apply the same techniques used to solve the equations for spinning strings to find the minimal surfaces describing a wide class of Wilson loops. We focus on different cases with periodic boundary conditions on the AdS_5 and S^5 factors and find a rich array of solutions. We examine the different phases that appear in the problem and comment on the applicability of integrability to the general problem.Comment: LaTex, 49 pages, 8 figure

A note on perturbation series in supersymmetric gauge theories

Exact results in supersymmetric Chern-Simons and N=2 Yang-Mills theories can be used to examine the quantum behavior of observables and the structure of the perturbative series. For the U(2) x U(2) ABJM model, we determine the asymptotic behavior of the perturbative series for the partition function and write it as a Borel transform. Similar results are obtained for N=2 SU(2) super Yang-Mills theory with four fundamental flavors and in N=2* super Yang-Mills theory, for the partition function as well as for the expectation values for Wilson loop and 't Hooft loop operators (in the 0 and 1 instanton sectors). In all examples, one has an alternate perturbation series where the coefficient of the nth term increases as n!, and the perturbation series are Borel summable. We also calculate the expectation value for a Wilson loop operator in the N=2* SU(N) theory at large N in different regimes of the 't Hooft gauge coupling and mass parameter. For large masses, the calculation reproduces the running gauge coupling for the pure N=2 SYM theory.Comment: 28 pages. V2: minor additions and reference adde

Semi-classical open string corrections and symmetric Wilson loops

In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric representation or a multiply wound one in N=4 super Yang-Mills theory. In order to distinguish the symmetric loop and the multiply wound loop, one should see an exponentially small correction in large 't Hooft coupling. We study semi-classically the disk open string attached to the D3-brane. We obtain the exponent of the term and it agrees with the result of the matrix model calculation of the symmetric Wilson loop.Comment: 14 pages, 4 figures. v2: explanation improved. v3: argument in section 2 is improved, result not change