Superconformal surfaces in four dimensions

Abstract

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Rényi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $\mathcal{N}=(2,2)$ surface defects in $\mathcal{N}⩾2$ superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.

60 pages; v3: matches published version

References in corpus (45)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal collider physics: Energy and charge correlations
• S-duality in N=2 supersymmetric gauge theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Universality of corner entanglement in conformal field theories
• Entanglement Entropy, Trace Anomalies and Holography
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• A non-renormalization theorem for chiral primary 3-point functions
• Bootstrapping the half-BPS line defect
• Instanton counting with a surface operator and the chain-saw quiver
• Entanglement entropy across a deformed sphere
• Universality at large transverse spin in defect CFT
• Universality in the geometric dependence of Renyi entropy
• An Analytic Approach to BCFT${}_d$
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• VOAs labelled by complex reflection groups and 4d SCFTs
• Twist operators in higher dimensions
• Bubbling Surface Operators And S-Duality
• Analytic Bootstrap for Boundary CFT
• Line defects and radiation in $\mathcal{N}=2$ theories
• Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS_7 x S^4
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Holographic Gauge Theories in Background Fields and Surface Operators
• Supersymmetric Rényi Entropy in Five Dimensions
• Free Field Realizations from the Higgs Branch
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• Schur correlation functions on $S^3\times S^1$
• Exact Bremsstrahlung functions in ABJM theory
• Holography of BPS surface operators
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Chiral Algebras, Localization and Surface Defects
• Renyi Entropy and Geometry
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Flavored surface defects in 4d N=1 SCFTs
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Superconformal Blocks: General Theory
• Marginal deformations and defect anomalies
• Defect multiplets of N=1 supersymmetry in 4d
• How a-type anomalies can depend on marginal couplings
• Surface operators in the Klebanov-Witten theory
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Emitted Radiation and Geometry
• Surface operators, dual quivers and contours
• An infrared bootstrap of the Schur index with surface defects

Cited by in corpus (34)

• Line and surface defects for the free scalar field
• 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${}^4$
• Surface Defect, Anomalies and $b$-Extremization
• Defect $a$-Theorem and $a$-Maximization
• A slow review of the AGT correspondence
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Monodromy Defects in Free Field Theories
• Analytic bootstrap for the localized magnetic field
• The exact Schur index in closed form
• Free energy and defect $C$-theorem in free scalar theory
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Conformal dispersion relations for defects and boundaries
• Holographic Line Defects in $D=4$, $N=2$ Gauged Supergravity
• Discreteness and Integrality in Conformal Field Theory
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Conformal Bootstrap near the edge
• Surface defects, flavored modular differential equations and modularity
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Interacting conformal scalar in a wedge
• Observations on BPS observables in 6d
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• Defect Conformal Blocks from Appell Functions
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Ironing out the crease
• Holographic Generalised Gukov-Witten Defects
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Complexity for superconformal primaries from BCH techniques
• Surface Operators in Superspace
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
• Shape Deformations of Charged Rényi Entropies from Holography