Secret symmetries in AdS/CFT

Leeuw, Marius de; Matsumoto, Takuya; Moriyama, Sanefumi; Regelskis, Vidas; Торриелли, Алессандро

doi:10.1088/0031-8949/86/02/028502

Cited by 18 publications

(16 citation statements)

References 77 publications

(156 reference statements)

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“…Apart from the Yangian Y rpsup2, 2|4qs symmetries [23,58], the S-matrix of N " 4 supersymmetric Yang-Mills theory has a so-called bonus symmetry [168], the level-1 recurrence of the hypercharge generator, which is itself not a symmetry. A similar situation has been observed before the discovery of the bonus symmetry for the AdS 5Ŝ 5 worldsheet S-matrix, which is Yangian invariant [169,170] and also exhibits an additional symmetry at level-1 [171][172][173], the so-called secret symmetry.…”

Section: Bonus Symmetriessupporting

confidence: 69%

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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Section: Bonus Symmetriessupporting

confidence: 69%

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Münkler

2018

Springer Theses

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“…They have also been observed in boundary scattering problems [17], n-point amplitudes [18], the pure-spinor formalism [19], in the quantum-affine deformations [20] and in the context of Wilson loops [21]. This makes it quite a significant feature of the system and not an isolated instance [22]. Some light on the problem was recently shed by applying the so-called RT T formulation [23].…”

Section: Quantum Group Symmetries In Ads/cf Tmentioning

confidence: 94%

q -Poincaré invariance of the AdS3/CFT2
Borsato
¹
,
Strömwall
²
,
Торриелли
³

2018
Phys. Rev. D
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We consider the exact R-matrix of AdS 3 /CFT 2 , which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds AdS 3 × S 3 × T 4 and AdS 3 × S 3 × S 3 × S 1 with pure Ramond-Ramond fluxes. We show that R is invariant under a "deformed boost" symmetry, for which we write an explicit exact coproduct, i.e. its action on two-particle states. When we include the boost, the symmetries of the R-matrix close into a q-Poincaré superalgebra. Our findings suggest that the recently discovered boost invariance in AdS 5 /CFT 4 may be a common feature of AdS/CFT systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the AdS 3 /CFT 2 classical r-matrix.

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“…The particular Yangian Y [psu(2, 2|4)] allows for further special features such as the occurence of so-called bonus or secret symmetries, see e.g [108]…”

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confidence: 99%

Lectures on Yangian symmetry

Loebbert

2016

J. Phys. A: Math. Theor.

108

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In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel'd's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the twodimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and N = 4 superconformal Yang-Mills theory in four dimensions. This review arose from lectures given at the Young Researchers Integrability School at Durham University (UK).

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Secret symmetries in AdS/CFT

Cited by 18 publications

References 77 publications

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

q -Poincaré invariance of the AdS3/CFT2
Borsato
¹
,
Strömwall
²
,
Торриелли
³

2018
Phys. Rev. D
Self Cite

Lectures on Yangian symmetry

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About

Secret symmetries in AdS/CFT

Cited by 18 publications

References 77 publications

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

q -Poincaré invariance of the AdS3/CFT2 Borsato1, Strömwall2, Торриелли3 2018Phys. Rev. DSelf Cite

Lectures on Yangian symmetry

Contact Info

Product

Resources

About

q -Poincaré invariance of the AdS3/CFT2
Borsato
¹
,
Strömwall
²
,
Торриелли
³

2018
Phys. Rev. D
Self Cite