Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$

Abstract

Correlators of local operators inserted on a straight Wilson loop in a conformal gauge theory have the structure of a one-dimensional "defect" CFT. As was shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacena loop in $\mathcal{N}=4$ SYM one can compute the strong-coupling contributions to 4-point correlators of operator insertions by starting with the AdS${}_5\times S^5$ string action expanded near the AdS${}_2$ minimal surface and evaluating the corresponding AdS${}_2$ Witten diagrams. We perform the analogous computations in the non-supersymmetric case of the standard Wilson loop with no coupling to the scalars. The corresponding non-supersymmetric "defect" CFT${}_1$ has an unbroken $SO(6)$ global symmetry. The elementary bosonic operators (6 SYM scalars and 3 components of the SYM field strength) are dual respectively to the $S^5$ embedding coordinates and AdS${}_5$ coordinates transverse to the minimal surface ending on the line at the boundary. The $SO(6)$ symmetry is preserved provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); one should then integrate over the $S^5$. The massless $S^5$ fluctuations have logarithmic propagator, corresponding to the boundary scalar operator having dimension $\Delta =\frac{5}{\sqrt{\lambda }}+\dots$ at strong coupling. The resulting functions of 1d cross-ratio in the 4-point functions have a more complicated structure than in the supersymmetric case, involving polylogs (Li${}_3$ and Li${}_2$). We also discuss consistency with the operator product expansion which allows extracting the leading strong coupling corrections to the anomalous dimensions of the operators appearing in the intermediate channels.

arXiv comment50 pages, 12 figures. v2: minor changes

References in corpus (47)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• AdS/CFT Correspondence and Symmetry Breaking
• Holography from Conformal Field Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• Comments on gluon scattering amplitudes via AdS/CFT
• Diving into traversable wormholes
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• Holographic Wilson Loops
• Solving the Simplest Theory of Quantum Gravity
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• Unitarity and the Holographic S-Matrix
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Conformal Partial Waves: Further Mathematical Results
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Generalized quark-antiquark potential at weak and strong coupling
• Defects in conformal field theory
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• Bootstrapping the half-BPS line defect
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Crossing Symmetry in Alpha Space
• The Spectrum of Excitations of Holographic Wilson Loops
• Gauge fields - strings duality and the loop equation
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Chaotic strings in AdS/CFT
• On semiclassical approximation and spinning string vertex operators in AdS_5 x S^5
• Line defects and radiation in $\mathcal{N}=2$ theories
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Wilson Loop Renormalization Group Flows
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Notes on Euclidean Wilson loops and Riemann Theta functions
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Precision matching of circular Wilson loops and strings in AdS(5)xS(5)
• Correlation functions of boundary field theory from bulk Green's functions and phases in the boundary theory
• Spin chain integrability in non-supersymmetric Wilson loops
• Exact momentum fluctuations of an accelerated quark in N=4 super Yang-Mills
• Holography of Non-relativistic String on AdS5xS5
• Defect multiplets of N=1 supersymmetry in 4d
• Structure constants of operators on the Wilson loop from integrability
• A defect action for Wilson loops

Cited by in corpus (35)

• Landau diagrams in AdS and S-matrices from conformal correlators
• CFT in AdS and boundary RG flows
• N=2 Conformal SYM theories at large N
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Fermions in AdS and Gross-Neveu BCFT
• On boundary correlators in Liouville theory on AdS${}_2$
• Wilson loop in general representation and RG flow in 1d defect QFT
• Supersymmetric Mixed Boundary Conditions in AdS${}_2$ and DCFT${}_1$ Marginal Deformations
• Supersymmetric Liouville theory in AdS${}_2$ and AdS/CFT
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Mellin amplitudes for 1$d$ CFT
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Non-abelian Toda theory on AdS${}_2$ and AdS${}_2$/CFT${}_2^{1/2}$ duality
• Boundary correlators in WZW model on AdS${}_2$
• On three-point functions in ABJM and the latitude Wilson loop
• Wilson loops and defect RG flows in ABJM
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Emitted Radiation and Geometry
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Interpolating Boundary Conditions on $Ad{S}_2$
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• On the abundance of supersymmetric strings in $Ad{S}_3\times S^3\times S^3\times S^1$ describing BPS line operators
• On anomalous conformal Ward identities for Wilson loops on polygon-like contours with circular edges
• Interpolating Bremsstrahlung function in ABJM
• 1d Conformal Field Theory and Dispersion Relations
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Flat limit of massless scalar scattering in ${\mathrm{AdS}}_2$
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM