Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

Beccaria, Matteo; Giombi, Simone; Tseytlin, Arkady A.

doi:10.1007/jhep01(2022)056

Cited by 15 publications

(26 citation statements)

References 32 publications

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“…In this paper we continue our investigation [1,2,3,4] of a family of operators that interpolate between the supersymmetric Wilson-Maldacena (ζ " 1) and the standard Wilson (ζ " 0) loop operators [5] W pζq pCq " Tr P exp…”

Section: Introductionmentioning

confidence: 96%

Wilson loop in general representation and RG flow in 1d defect QFT

Beccaria,

Giombi,

Tseytlin

2022

Preprint

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The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in N " 4 SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter ζ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank k symmetric representation of SU pN q, we also consider a certain "semiclassical" limit where k is taken to infinity with the product k ζ 2 fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the large k limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG flow and comment on the consistency of the results with the 1d defect version of the F-theorem.

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Section: Introductionmentioning

confidence: 96%

Wilson loop in general representation and RG flow in 1d defect QFT

Beccaria,

Giombi,

Tseytlin

2022

Preprint

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“…Our analysis is most directly similar to the one in [59], where the action is also computed with a DGO boundary term added to the Nambu-Goto action. 27 In that paper, the DGO term is written not as a bulk integral of a total derivative like in eq. (4.26), which would give contributions from both boundaries, but rather as a boundary integral over only the boundary incident on the Wilson loop.…”

Section: Jhep03(2022)020mentioning

confidence: 99%

“…It can be thought as the IR fixed point of a RG flow which starts in the UV from the ordinary, non-supersymmetric Wilson loop[22][23][24]. See also[25][26][27] for related work.2 In[28] a general solution parametrized by two cusp angles was considered. Here we focus on the case where both angles are zero, which corresponds to insertions on a straight line or circular loop.…”

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confidence: 99%

Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM: matrix model and classical string

Giombi

Komatsu

Offertaler

2022

J. High Energ. Phys.

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We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/$$ \sqrt{\lambda } $$ λ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 $$ \mathcal{N} $$ N = 2 superconformal field theories, but our results hold also for non-extremal cases.

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“…) 37 Here sdet stands for the super-determinant. 38 Precisely speaking, the cuts corresponding to fermionic excitations in (6.7) are infinitesimal: namely they are poles rather than branch cuts.…”

Section: Classical Integrability Spectral Curve and Quasi-momentummentioning

confidence: 99%

“…Furthermore, the half-BPS Wilson loop provides a simple example of defect renormalization group flow, which connects the ordinary Wilson loop without scalar couplings to the half-BPS loop [34]. The defect renormalization group flow can be studied both at weak and strong couplings [35,36] (see also [37][38][39] for related recent works) and it allows one to explicitly check the monotonicity of the defect entropy, which was proven recently in [40].…”

Section: Introductionmentioning

confidence: 99%

Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve

Giombi,

Komatsu,

Offertaler

2022

Preprint

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We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the 't Hooft coupling λ are sent to infinity with the ratio J/ √ λ fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green's functions on the worldsheet. We derive a representation of the Green's functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green's functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

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Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

Cited by 15 publications

References 32 publications

Wilson loop in general representation and RG flow in 1d defect QFT

Wilson loop in general representation and RG flow in 1d defect QFT

Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM: matrix model and classical string

Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve

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