For $SU(N)$ superconformal QCD we perform a three-loop calculation of the generalized cusp anomalous dimension of the BPS Wilson loop operator using HQET formalism. We obtain an expression which is valid at generic geometric and internal angles and f
inite gauge group rank $N$. For equal and opposite angles this expression vanishes, proving that at these points the cusp becomes BPS. From its small angle expansion we derive the corresponding Bremsstrahlung function at three loops, matching the matrix model prediction given in terms of derivatives of the Wilson loop on the ellipsoid. Finally, we discuss possible scenarios at higher loops, with respect to the existence of a universal effective coupling in an integrable subsector of the model.
In $mathcal N geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomolnyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson l
oops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in $mathcal N = 4$ orbifold ABJM theory. In the particular case of $mathcal N = 2$ orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.
We construct new families of 1/4 BPS Wilson loops in circular quiver $mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scal
ar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops. The new operators are cohomologically equivalent to bosonic 1/4 BPS Wilson loops and are then amenable of exact evaluation via localization techniques. Moreover, in the case of orbifold ABJM theory we identify the corresponding gravity duals for some of the 1/4 and 1/2 BPS Wilson loops.
This is a sequel of our paper hep-th/0606125 in which we have studied the {cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {cal N}=4 theory, with a complex deformation parameter beta and in the planar limit. There we have addresse
d the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter beta. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.
We study the cal{N}=1 SU(N) SYM theory which is a marginal deformation of the cal{N}=4 theory, with a complex deformation parameter beta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finitene
ss requires reality of the deformation parameter beta.
In the beta-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O_J = Tr(Phi_i^J Phi_k), i eq k and compute their exact anomalous dimensions for N,Jtoinfty. This leads to a prediction for the masses of the correspondin
g states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one--loop condition g^2=hbar{h} for superconformal invariance is indeed sufficient to insure the {em exact} superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The O_J sector of this theory shares many similarities with the BMN sector of the N=4 theory in the large R--charge limit.
We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the beta-deformed N=4 SYM. In particular we focus on the CPO Tr(Phi_1^2) and the operator Tr(Phi_1 Phi_2) not presently listed as BPS. We find
that for both operators no anomalous dimension is generated at this order, then confirming the results recently obtained in hep-th/0506128. However, in both cases a finite correction to the two-point function appears.
In a {cal N}=1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in {cal N}=4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the couplin
g constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/epsilon^2 pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g^2. We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results.
