Bootstrapping line defects in $\mathcal{N}=2$ theories

Abstract

We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^{\ast }|2)$ symmetry. In order to study correlation functions we construct a suitable superspace, and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After setting up the crossing equations we proceed with a numerical and analytical bootstrap analysis. We obtain numerical bounds on the CFT data and compare them to known solutions. We also present an analytic perturbative solution to the crossing equations, and argue that this solution captures line defects in $\mathcal{N}=2$ gauge theories at strong coupling.

arXiv comment42 pages, 6 figures

References in corpus (56)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Bounding scalar operator dimensions in 4D CFT
• Holography from Conformal Field Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Reading between the lines of four-dimensional gauge theories
• Bootstrapping the O(N) Vector Models
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Carving Out the Space of 4D CFTs
• Unitarity and the Holographic S-Matrix
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Bootstrapping the 3d Ising twist defect
• Exact results for the entanglement entropy and the energy radiated by a quark
• A spacetime derivation of the Lorentzian OPE inversion formula
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• The $\mathcal{N}=2$ superconformal bootstrap
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Defects in conformal field theory
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Bootstrapping the half-BPS line defect
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Unmixing Supergravity
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• A tauberian theorem for the conformal bootstrap
• Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
• Superconformal Symmetry and Correlation Functions
• Infrared Computations of Defect Schur Indices
• Universality at large transverse spin in defect CFT
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories
• Covariant Approaches to Superconformal Blocks
• Analytic Bootstrap for Boundary CFT
• Line defects and radiation in $\mathcal{N}=2$ theories
• PyCFTBoot: A flexible interface for the conformal bootstrap
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• Current OPEs in Superconformal Theories
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• A Crossing-Symmetric OPE Inversion Formula
• Long Multiplet Bootstrap
• On the Positive Geometry of Conformal Field Theory
• Exact Bremsstrahlung functions in ABJM theory
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Superconformal partial waves in Grassmannian field theories
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Revisiting N=4 superconformal blocks
• Superconformal Blocks: General Theory
• 2d small N=4 Long-multiplet superconformal block
• Deformations of the circular Wilson loop and spectral (in)dependence
• Towards general super Casimir equations for $4D$ $\mathcal{N}=1$ SCFTs

Cited by in corpus (23)

• Superconformal surfaces in four dimensions
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• 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${}^4$
• Bootstrapping line defects with $O(2)$ global symmetry
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• New Developments in the Numerical Conformal Bootstrap
• A slow review of the AGT correspondence
• Analytic bootstrap for the localized magnetic field
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Conformal dispersion relations for defects and boundaries
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Bootstrapping Coulomb and Higgs branch operators
• Defect Conformal Blocks from Appell Functions
• Universal Spinning Casimir Equations and Their Solutions
• Bootstrapping (D, D) Conformal Matter
• 1d Conformal Field Theory and Dispersion Relations
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs
• Universal sectors in superconformal defects
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM