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Register a new userDeformations of the circular Wilson loop and spectral (in)dependence
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In this paper we study the expectation value of deformations of the circular Wilson loop in ${cal N}=4$ super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from supersymmetric localization, so our focus is on deformations at higher orders. We find simple expressions for the expectation values for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. We also present a very simple algorithm (not requiring integration) to evaluate the two-loop result. We find that an exact symmetry of the strong coupling sigma-model, known as the spectral-parameter independence, is an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation. Furthermore, we find very simple patterns for how the spectral parameter can appear in the weak coupling calculation, suggesting all-order structures.
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We study string quantum corrections to the ratio of latitude and circular Wilson loops in N=4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS(5)xS(5) is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field-theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluating phaseshifts for all the fluctuation modes.
We consider the correlation function of a circular Wilson loop with two local scalar operators at generic 4-positions in planar N=4 supersymmetric gauge theory. We show that such correlator is fixed by conformal invariance up to a function of t Hooft coupling and two scalar combinations of the positions invariant under the conformal transformations preserving the circle. We compute this function at leading orders at weak and strong coupling for some simple choices of local BPS operators. We also check that correlators of an infinite line Wilson loop with local operators are the same as those for the circular loop.
We compute the one-loop correction to the probe D3-brane action in AdS5 x S5 expanded around the classical Drukker-Fiol solution ending on a circle at the boundary. It is given essentially by the logarithm of the one-loop partition function of an Abelian ${cal N}=4$ vector multiplet in AdS2 x S2 geometry. This one-loop correction is expected to describe the subleading 1/N term in the expectation value of circular Wilson loop in the totally symmetric rank k representation in SU(N) SYM theory at strong coupling. In the limit k << N when the circular Wilson loop expectation values for the symmetric representation and for the product of k fundamental representations are expected to match we find that this one-loop D3-brane correction agrees with the gauge theory result for the k-fundamental case.
We compute the one-loop world-sheet correction to partition function of $AdS_5 times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
We perform exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite t Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. In particular, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.
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