Exacting 𝒩 = 4 superconformal symmetry

Bargheer, Till; Beisert, Niklas; Galleas, W.; Loebbert, Florian; McLoughlin, Tristan

doi:10.1088/1126-6708/2009/11/056

Cited by 100 publications

(199 citation statements)

References 78 publications

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“…This symmetry was proven at tree-level in [15]. It is broken beyond tree-level [16,17] as will be discussed in more detail later.…”

Section: Introductionmentioning

confidence: 80%

“…17 Of course, presented like this, Grassmann analyticity seems to be a property of only one projection (the highest weight) W ++ of the six-plet W AB , the others do not have it. Also, the price for exhibiting this property of W ++ was breaking SU(4).…”

Section: The N = 4 Chiral Vector Multiplet As a 1/2 Bps Multipletmentioning

confidence: 88%

“…One can show that all tree-level super-amplitudes enjoy the dual superconformal symmetry P SU(2, 2|4) acting in the dual superspace [15,38]. At loop level, the super-amplitude divided by the MHV amplitude is expected to conserve its dual conformal symmetry 4 , while the anti-chiral half of dual Poincaré supersymmetry is broken [16,17].…”

Section: New Proposal: Super-correlators/super-amplitudes Dualitymentioning

confidence: 99%

“…However, the other halves of these supersymmetries (Q and S) are broken beyond tree level. The origin of this symmetry breaking can be traced back to the so-called holomorphic anomaly [16,17,48]. Unlike the K−anomaly, the correspondingQ− and S−anomalies are only known at one-loop level.…”

Section: (211)mentioning

confidence: 99%

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The super-correlator/super-amplitude duality: Part I

Eden

Heslop

Korchemsky³

et al. 2013

Nuclear Physics B

116

186

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We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N = 4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n−point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator.

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“…This symmetry was proven at tree-level in [15]. It is broken beyond tree-level [16,17] as will be discussed in more detail later.…”

Section: Introductionmentioning

confidence: 80%

Section: The N = 4 Chiral Vector Multiplet As a 1/2 Bps Multipletmentioning

confidence: 88%

Section: New Proposal: Super-correlators/super-amplitudes Dualitymentioning

confidence: 99%

Section: (211)mentioning

confidence: 99%

See 2 more Smart Citations

The super-correlator/super-amplitude duality: Part I

Eden

Heslop

Korchemsky³

et al. 2013

Nuclear Physics B

116

186

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“…A similar understanding of the full Yangian symmetry at loop level is still lacking and subject to ongoing research [15][16][17][18]. Recently it was argued that the (unregulated) loop integrand has the full Yangian symmetry, up to total derivatives [19] .…”

Section: Jhep04(2011)083 1 Introductionmentioning

confidence: 99%

New differential equations for on-shell loop integrals

Drummond

Henn

Trnka

2011

J. High Energ. Phys.

155

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We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N = 4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N = 4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.

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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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Exacting 𝒩 = 4 superconformal symmetry

Cited by 100 publications

References 78 publications

The super-correlator/super-amplitude duality: Part I

The super-correlator/super-amplitude duality: Part I

New differential equations for on-shell loop integrals

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

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