Bootstrapping the half-BPS line defect CFT in N = 4 supersymmetric Yang-Mills theory at strong coupling

We define a Mellin amplitude for CFT1 four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform. The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples. We then consider the perturbative setup produced by quartic interactions with an arbitrary number of derivatives in a bulk AdS2 field theory. With our formalism, we obtain a closed-form expression for the Mellin transform of tree-level contact interactions and for the first correction to the scaling dimension of “two-particle” operators exchanged in the generalized free field theory correlator.

Section: Introduction and Discussionmentioning

confidence: 99%

Section: Jhep10(2021)095mentioning

confidence: 99%

Mellin amplitudes for 1d CFT

Bianchi

Bliard

Форини

et al. 2021

“…(2.1) can be generalized to a 1/8−BPS Wilson loop [42,43], W 1/8 , whose contour x µ (ϕ) is any closed curve on the two-sphere x 2 1 + x 2 2 + x 2 3 = 1 and which couples to the scalars as Φ × x • d x, where x ≡ (x 1 , x 2 , x 3 ) and Φ ≡ (Φ 3 , −Φ 4 , Φ 6 ). 15 The expectation value of W 1/8 is found by replacing g → g A(4π−A) 4π 2 in eq. (2.2), where A is the area of one of the two regions of the two-sphere demarcated by the contour.…”

Section: Large Charge Correlators From the Bremsstrahlung Functionmentioning

confidence: 99%

“…In this way the higher charge topological operators define an orthogonal basis that can be constructed from non-coincident insertions of the unit topological operators using the Gram-Schmidt procedure. 15 We pick this combination of scalar fields to couple to the 1/8-BPS Wilson loop in order to match our conventions for the half-BPS Wilson loop and topological operators in section 2. 16 More generally, we may equivalently define the topological operator to be x(ϕ) • Φ + in • Φ ⊥ , where…”

Section: Large Charge Correlators From the Bremsstrahlung Functionmentioning

confidence: 99%

“…Here SL(2, R) is the 1d conformal symmetry preserved by a circle (or line), SO(3) is the symmetry under spacetime rotations transverse to the defect, and SO (5) is the residual R-symmetry that rotates the five scalars that do not couple to the Wilson loop. The correlation functions of operator insertions on the Wilson loop (together with correlation functions involving "bulk" single-trace operators) define a rather rich defect CFT that is amenable to studies via holography [9][10][11], localization [11][12][13], conformal bootstrap [14][15][16] and integrability [9,[17][18][19][20][21]. 1 A Wilson loop operator in the fundamental representation is dual to an open string minimal surface extending in AdS and ending at the boundary on the contour that defines the loop operator.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Giombi

Komatsu

Offertaler

2022

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.

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

Beccaria

Giombi

Tseytlin

2022

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.