Generalized quark‐antiquark potential in AdS/CFT

Abstract

Key words AdS/CFT correspondence, supersymmetric gauge theory.In this talk we present a family of Wilson loop operators which continuously interpolates between the 1/2 BPS line and the antiparallel lines, and can be thought of as calculating a generalization of the quarkantiquark potential for the gauge theory on S 3 × R. We evaluate the first two orders of these loops perturbatively both in the gauge and string theory. We obtain analytical expressions in a systematic expansion around the 1/2 BPS configuration, and comment on possible all-loop patterns for these Wilson loops.Copyright line will be provided by the publisher OverviewOne of the most fundamental observables in a quantum field theory is the potential between charged particles, which in a gauge theory is captured by a long rectangular Wilson loop, or a pair of antiparallel lines representing the trajectories of infinitely heavy quarks. Such quark-antiquark potential can be also considered in the maximally supersymmetric N = 4 SYM theory, where "quarks" are modeled by infinitely massive W-bosons arising from a Higgs mechanism [1].The expectation value of this observable was calculated very early after the introduction of the AdS/CFT correspondence by the effective action of a string ending along the curve on the four-dimensional AdS boundary, and is in fact a seminal example of the duality itself. In this context of a conformal field theory the potential is fixed to be Coulomb-like and the whole dynamical content is in the corresponding coefficient, for which the weak and strong coupling ('t Hooft coupling λ) previously obtained results readAbove, L is the distance between the lines, K is the complete elliptic integral of the first kind and the weakcoupling expansion is the field-theoretical calculation of [2,3,4]. On the string theory (strong coupling) side, the question of evaluating the first quantum string correction a 1 to the classical result of [1] 1 is a hard mathematical problem. The absence of parameters in the problem (the only one, L, being fixed by conformal invariance) precludes considering special scaling limits in which nice results in σ-model perturbation theory have been obtained for some relevant string solutions (see, for example, [6,7] and reference therein). The coefficient a 1 was presented formally in [8,9], evaluated numerically in [10] to be a 1 = 1.33459 and simplified further in [11] to an analytic one-dimensional integral representation. * Corresponding author vforini@icc.ub.edu * * nadav.drukker@kcl.ac.uk 1 This is actually the AdS 5 ×S 5 counterpart of the so-called "Lüscher term", which in flat space is a coulombic term proportional to the number of transverse dimensions [5].

One-loop corrections to a holographic Wilson loop in AdS 4 × ℂℙ3

“…Although we only studied circular Wilson loops in detail here, (16) Yang-Mills theory was studied in [27,28]. It is also pointed out that the angle dependence of general BPS Wilson loop operators can be related to interesting physical quantities such as cusp anomalous dimension, radiation emitted by a moving quark etc.…”

“…Eq. (28) will be used for non-zero modes, while for the zero-modes we take Neumann boundary conditions at L, and we need to use ψ (b)/ψ 0 (b) instead on the right hand side of (28).…”