Small deformations of supersymmetric Wilson loops and open spin-chains

Drukker, Nadav; Kawamoto, Shoichi

doi:10.1088/1126-6708/2006/07/024

Cited by 112 publications

(224 citation statements)

References 79 publications

(111 reference statements)

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“…Those operators preserve the regular Poincaré supersymmetries and have trivial expectation values [19,20], but there should be many more supersymmetric Wilson loops which preserve other combinations of the regular and conformal supersymmetry generators. Those include the ones studied in this paper as well as some deformations of the line or circle by insertion of local operators as in [21]. There is a very rich structure of supersymmetric Wilson loops that is worth exploring.…”

Section: Discussionmentioning

confidence: 99%

1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

Drukker¹

2006

J. High Energy Phys.

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The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple example studied in this paper, where there are two 1/4 BPS string solutions, one a minimum and the other not. Like in the case of the regular circular loop the perturbative expansion seems to be captured by a free matrix model. This gives enough analytic control to extrapolate from weak to strong coupling and find both saddle points in the asymptotic expansion of the matrix model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson loop operators.

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Section: Discussionmentioning

confidence: 99%

1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

Drukker¹

2006

J. High Energy Phys.

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230

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“…It is of interest to relate the expression (2.67) to what is known about 2-point functions of (scalar) operators on the line or circle (see [3,5,6,[30][31][32][33][34]). Let us choose the scalar coupling in (1.1) to be along 6-th direction, i.e.…”

Section: Jhep03(2018)131 3 Relation To Correlators Of Scalar Operatormentioning

confidence: 99%

Non-supersymmetric Wilson loop in $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT

Beccaria

Giombi

Tseytlin

2018

J. High Energ. Phys.

170

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Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized Wilson loop operator containing a constant parameter ζ in front of the scalar coupling term, so that ζ = 0 corresponds to the standard Wilson loop, while ζ = 1 to the locally supersymmetric one. We compute the expectation value of this operator for circular loop as a function of ζ to second order in the planar weak coupling expansion in N = 4 SYM theory. We then explain the relation of the expansion near the two conformal points ζ = 0 and ζ = 1 to the correlators of scalar operators inserted on the loop. We also discuss the AdS 5 × S 5 string 1-loop correction to the strong-coupling expansion of the standard circular Wilson loop, as well as its generalization to the case of mixed boundary conditions on the five-sphere coordinates, corresponding to general ζ. From the point of view of the defect CFT 1 defined on the Wilson line, the ζ-dependent term can be seen as a perturbation driving a RG flow from the standard Wilson loop in the UV to the supersymmetric Wilson loop in the IR. Both at weak and strong coupling we find that the logarithm of the expectation value of the standard Wilson loop for the circular contour is larger than that of the supersymmetric one, which appears to be in agreement with the 1d analog of the F-theorem.

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“…The quantity Γ L , which we will call the cusp anomalous dimension, will be the main object of our studies. When θ 2 − φ 2 = 0 the observable W L becomes BPS and the cusp anomalous dimension vanishes [20]. In [9] the anomalous dimension in the near-BPS limit θ = 0, φ → 0 was calculated using the method of Y-system or Thermodynamical Bethe Ansatz [21][22][23].…”

Section: Cusp Anomalous Dimension Of a Wilson Linementioning

confidence: 99%

Algebraic curve for a cusped Wilson line

Sizov

Valatka

2014

J. High Energ. Phys.

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We consider the classical limit of the recently obtained exact near-BPS result for the anomalous dimension of a cusped Wilson line with the insertion of an operator with L units of R-charge at the cusp in planar N = 4 SYM. The classical limit requires taking both the 't Hooft coupling and L to infinity. Since the formula for the cusp anomalous dimension involves determinants of size proportional to L, the classical limit requires a matrix model reformulation of the result. Building on results of Gromov and Sever, we construct such a matrix model-like representation and find the corresponding classical algebraic curve. Using this we find the classical value of the cusp anomalous dimension and the 1-loop correction to it. We check our results against the energy of the classical solution and numerically by extrapolating from the quantum regime of finite L.

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Small deformations of supersymmetric Wilson loops and open spin-chains

Cited by 112 publications

References 79 publications

1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

Non-supersymmetric Wilson loop in $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT

Algebraic curve for a cusped Wilson line

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