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

Giombi, Simone; Komatsu, Shota; Offertaler, Bendeguz

doi:10.1007/jhep03(2022)020

Cited by 19 publications

(35 citation statements)

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“…In this regime, the role of the large charge effective field theory is played by a probe string action in AdS 5 × S 5 , which becomes classical in the large J limit. As we demonstrated in the previous paper [41], the leading large charge answer for the correlation functions can be computed by evaluating light vertex operators on a nontrivial classical string solution with large angular momentum, which was constructed in [8,49,50]. In special kinematics, we can compare the results from holography with exact results from supersymmetric localization [14] and verify the agreement of the two approaches.…”

Section: Introductionmentioning

confidence: 58%

“…(2.11) because, at leading order in large charge, the topological primary truncates to a sum of powers of Z and Z only-namely, Φ ∼ ( Z (t)Z(t) + Z (t) Z(t)) for an appropriate choice of Z , Z . Correlators of the topological operators can be studied using localization [14,15] and, accordingly, in [41] we expressed the topological correlators in terms of an "emergent"…”

Section: Preliminariesmentioning

confidence: 99%

“…We reviewed the classical string dual to the Wilson loop with Z J and ZJ in [41], which was discussed previously in [8,49,50]. We computed the action and the vertex operators dual to Z and Z on the classical solution, which determined the leading large charge behavior of the two-point and higher-point functions in (2.9) and (2.11).…”

Section: Previewmentioning

confidence: 99%

“…This configuration in global coordinates has manifest translational symmetry along τ . The classical string dual to this operator was discussed in [8,49,50] and reviewed in [41]. To summarize, the string forms a strip in AdS 5 that stretches between the two antipodal lines at ρ → ±∞ and partly wraps an S 2 in S 5 , carrying angular momentum J.…”

Section: Quadratic Action For the Fluctuationsmentioning

confidence: 99%

“…The goal of this paper and its companion [41] is to explore a connection to yet another non-perturbative approach-the large charge expansion of conformal field theory. Starting from the seminal works [42,43], general properties of the large charge sector in interacting CFTs with global symmetries have been actively explored in recent years using effective field theory techniques and treating the inverse of the charge as a small expansion parameter [44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 58%

Section: Preliminariesmentioning

confidence: 99%

Section: Previewmentioning

confidence: 99%

Section: Quadratic Action For the Fluctuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Giombi,

Komatsu,

Offertaler

2022

Preprint

Self Cite

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Large charge ’t Hooft limit of $$ \mathcal{N} $$ = 4 super-Yang-Mills

Caetano,

Komatsu,

Wang

2024

J. High Energ. Phys.

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The planar integrability of $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) is the cornerstone for numerous exact observables. We show that the large charge sector of the SU(2) $$ \mathcal{N} $$ N = 4 SYM provides another interesting solvable corner which exhibits striking similarities despite being far from the planar limit. We study non-BPS operators obtained by small deformations of half-BPS operators with R-charge J in the limit J → ∞ with $$ {\lambda}_J\equiv {g}_{\textrm{YM}}^2J/2 $$ λ J ≡ g YM 2 J / 2 fixed. The dynamics in this large charge ’t Hooft limit is constrained by a centrally-extended $$ \mathfrak{psu} $$ psu (2|2)2 symmetry that played a crucial role for the planar integrability. To the leading order in 1/J, the spectrum is fully fixed by this symmetry, manifesting the magnon dispersion relation familiar from the planar limit, while it is constrained up to a few constants at the next order. We also determine the structure constant of two large charge operators and the Konishi operator, revealing a rich structure interpolating between the perturbative series at weak coupling and the worldline instantons at strong coupling. In addition we compute heavy-heavy-light-light (HHLL) four-point functions of half-BPS operators in terms of resummed conformal integrals and recast them into an integral form reminiscent of the hexagon formalism in the planar limit. For general SU(N) gauge groups, we study integrated HHLL correlators by supersymmetric localization and identify a dual matrix model of size J/2 that reproduces our large charge result at N = 2. Finally we discuss a relation to the physics on the Coulomb branch and explain how the dilaton Ward identity emerges from a limit of the conformal block expansion. We comment on generalizations including the large spin ’t Hooft limit, the combined large N-large J limits, and applications to general $$ \mathcal{N} $$ N = 2 superconformal field theories.

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Nonrelativistic CFTs at large charge: Casimir energy and logarithmic enhancements

Hellerman

Orlando

Pellizzani

et al. 2022

J. High Energ. Phys.

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The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFTs can be held to experimental verification. Here, we examine the structure of conformal dimensions of charge-Q operators in nonrelativistic CFTs, in the large-Q regime, from the non-linear sigma model perspective. We discuss in detail the renormalization of edge divergences using dimensional regularization, elucidating the presence of log(Q) terms in the large-charge expansion. Finally, we use dimensional regularization to compute the universal one-loop Q0 log Q contribution to the ground-state energy in d = 3 spatial dimensions, with the result $$ \Delta {(Q)}_{Q^0}=\frac{1}{3\sqrt{3}}\log (Q)+ $$ Δ Q Q 0 = 1 3 3 log Q + const.

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

Cited by 19 publications

References 60 publications

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

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

Large charge ’t Hooft limit of $$ \mathcal{N} $$ = 4 super-Yang-Mills

Nonrelativistic CFTs at large charge: Casimir energy and logarithmic enhancements

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