The cusp anomalous dimension at three loops and beyond

Correa, Diego H.; Henn, Johannes M.; Maldacena, Juan; Sever, Amit

doi:10.1007/jhep05(2012)098

Cited by 121 publications

(282 citation statements)

References 57 publications

(177 reference statements)

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“…Here we computed explicitly the three-loop contributions to the soft anomalous dimension of a product of nonlightlike Wilson lines from a specific class of webs consisting of multiple gluon exchanges which connect four lines, the 1-2-2-1 and the 1-1-1-3 webs. These are the first threeloop results to become available beyond the case of the angle-dependent cusp anomalous dimension which was studied recently in the context of the N = 4 theory [4,16,[82][83][84]. Our final results for these webs, presented in section 5, display a remarkably simple structure involving a pure function of weight 5, which is a sum of products of specific polylogarithmic functions, each depending on a single cusp angle.…”

Section: Discussionmentioning

confidence: 59%

“…While progress on this front was largely restricted to (planar) N = 4 supersymmetric Yang-Mills theory, e.g. [76][77][78][79][80][81][82][83][84][85], where amplitudes appear to be directly related to certain Wilson loops, infrared singularities are generally similar across all gauge theories and can be computed by considering products of Wilson-line operators.…”

Section: Jhep04(2014)044mentioning

confidence: 99%

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From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1/α ij , at the level of the symbol the result also admits a crossing symmetry α ij → −α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and 1 − α 2 ij . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

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Section: Discussionmentioning

confidence: 59%

Section: Jhep04(2014)044mentioning

confidence: 99%

From webs to polylogarithms

Gardi

2014

J. High Energ. Phys.

186

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“…The first three orders were known completely and were computed in [1,[3][4][5][6][7][8]. In addition, our formula (3.18) matches the all-orders prediction of [3] for the coefficients of the leading logarithmic termsĝ 2n log n−1ĝ .…”

Section: Jhep12(2016)122mentioning

confidence: 57%

“…In the following sections we will solve these equations both analytically at weak coupling to a high order and numerically in a wide range of the coupling. We will be also able to demonstrate how in a special limit the QSC reduces to the Schrödinger equation of [1,4] resumming the ladder diagrams to all orders in perturbation theory.…”

Section: Jhep12(2016)122mentioning

confidence: 95%

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Quark-anti-quark potential in N $$ \mathcal{N} $$ = 4 SYM

Gromov

Levkovich-Maslyuk

2016

J. High Energ. Phys.

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We construct a closed system of equations describing the quark-anti-quark potential at any coupling in planar N = 4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion.Moreover, we study analytically the generalized quark-anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.

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Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Münkler

2018

Springer Theses

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This thesis discusses hidden symmetries within N " 4 supersymmetric Yang-Mills theory or its AdS/CFT dual, string theory in AdS 5ˆS 5 . Here, we focus on the Maldacena-Wilson loop, which is a suitable object for this study since its vacuum expectation value is finite for smooth contours and the conjectured duality to scattering amplitudes provides a conceptual path to transfer its symmetries to other observables. Its strong-coupling description via minimal surfaces in AdS 5 allows to construct the symmetries from the integrability of the underlying classical string theory. This approach has been utilized before to derive a strong-coupling Yangian symmetry of the Maldacena-Wilson loop and describe equiareal deformations of minimal surfaces in AdS 3 . These two findings are connected and extended in the present thesis.In order to discuss the symmetries systematically, we first discuss the symmetry structure of the underlying string model. The discussion can be generalized to the discussion of generic symmetric space models. For these, we find that the symmetry which generates the equiareal deformations of minimal surfaces in AdS 3 has a central role in the symmetry structure of the model: It acts as a raising operator on the infinite tower of conserved charges, thus generating the spectral parameter, and can be employed to construct all symmetry variations from the global symmetry of the model. It is thus referred to as the master symmetry of symmetric space models. Additionally, the algebra of the symmetry variations and the conserved charges is worked out.For the concrete case of minimal surfaces in AdS 5 , we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The results leads to a couplingdependent generalization of the master symmetry, which constitutes a symmetry of the Maldacena-Wilson loop at any value of the coupling constant. Our discussion clarifies why previous attempts to transfer the deformations of minimal surfaces in AdS 3 to weak coupling were unsuccessful. We discuss several attempts to transfer the Yangian symmetry to weak or arbitrary coupling, but ultimately conclude that a Yangian symmetry of the Maldacena-Wilson loop seems not to be present.The situation changes when we consider Wilson loops in superspace, which are the natural supersymmetric generalizations of the Maldacena-Wilson loop. Substantial evidence for the Yangian invariance of their vacuum expectation value has been provided at weak coupling and the description of the operator as well as its weak-coupling Yangian invariance were subsequently established in parallel to the work on this thesis. We discuss the strong-coupling counterpart of this finding, where the Wilson loop in superspace is described by minimal surfaces in the superspace of type IIB superstring theory i...

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The cusp anomalous dimension at three loops and beyond

Cited by 121 publications

References 57 publications

From webs to polylogarithms

From webs to polylogarithms

Quark-anti-quark potential in N $$ \mathcal{N} $$ = 4 SYM

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

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