Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills

Giombi, Simone; Komatsu, Shota

doi:10.1007/jhep06(2020)075

Cited by 4 publications

(24 citation statements)

References 73 publications

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“…The defect CFT defined by the 1/2-BPS Wilson loop contains a supersymmetric subsector whose correlation functions are position-independent [23,24,52,[67][68][69]. For the Wilson loops in the fundamental representation, such correlators were computed exactly using the supersymmetric localization 4 in [23,24].…”

Section: /8 Bps Wilson Loops and Topological Sectormentioning

confidence: 99%

“…In this section, we discuss a representation [52,68] for the expectation value of the BPS Wilson loop in which the area dependence appears only in the exponent. 6 Using such a representation and the loop equation in 2d Yang-Mills, new results for intersecting Wilson loops were derived in [52]. Below we review its derivation for the fundamental Wilson loops and generalize it to the higher-rank Wilson loops.…”

Section: Jhep11(2020)064 3 Multiple Integral Representation Of the 1/mentioning

confidence: 99%

“…The action (3.1) can be viewed as a matrix-model analogue of the BF-theory representation of the 2d Yang-Mills theory: namely, we can derive (3.1) from the action of the 2d Yang-Mills by identifying B Σm and X j with constant modes of B and * F respectively. See [52,68] for more details.…”

Section: Partition Function and Fundamental Loopsmentioning

confidence: 99%

“…was solved by first integrating out B fields and reducing it to a Gaussian matrix model. To derive the representation in [52], we instead integrate out X and reduce it to a matrix model of the B fields. The integration of the X field can be performed by the use of the Harish-Chandra-Itzykson-Zuber integral, dΩ e itr[Ω † AΩB] = det e ia i b j ∆(a)∆(b) , (3.5) where A and B are diagonal matrices with eigenvalues a j 's and b j 's, Ω is an element of the unitary group, and ∆ is a Vandermonde factor ∆(a) ≡ i<j (a i −a j ).…”

Section: Partition Function and Fundamental Loopsmentioning

confidence: 99%

“…To overcome this problem, we first consider generalizations of the higher-rank Wilson loops that couple to several different areas. The expectation values of such Wilson loops can be computed by the application of the loop equation in two-dimensional Yang-Mills theory as shown in [52]. The results are given by multiple contour integrals, which are similar but different from the eigenvalue integrals of the matrix models.…”

Section: Jhep11(2020)064 Introductionmentioning

confidence: 99%

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Giant Wilson loops and AdS2/dCFT1

Giombi

Jiang

Komatsu

2020

J. High Energ. Phys.

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The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

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Section: /8 Bps Wilson Loops and Topological Sectormentioning

confidence: 99%

Section: Jhep11(2020)064 3 Multiple Integral Representation Of the 1/mentioning

confidence: 99%

Section: Partition Function and Fundamental Loopsmentioning

confidence: 99%

Section: Partition Function and Fundamental Loopsmentioning

confidence: 99%

Section: Jhep11(2020)064 Introductionmentioning

confidence: 99%

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Giant Wilson loops and AdS2/dCFT1

Giombi

Jiang

Komatsu

2020

J. High Energ. Phys.

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Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

Giombi

Komatsu

Offertaler

2022

J. High Energ. Phys.

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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 $$ \mathcal{N} $$ 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/$$ \sqrt{\lambda } $$ 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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Giant Wilson Loops and AdS$_2$/dCFT$_1$

Giombi,

Jiang,

Komatsu

2020

Preprint

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The 1/2-BPS Wilson loop in N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS 2 × S 2 and AdS 2 × S 4 worldvolume geometries, ending at the AdS 5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the 't Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three-and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

show abstract

Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills

Cited by 4 publications

References 73 publications

Giant Wilson loops and AdS2/dCFT1

Giant Wilson loops and AdS2/dCFT1

Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

Giant Wilson Loops and AdS$_2$/dCFT$_1$

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