Central Charges of 2d Superconformal Defects

Abstract

In conformal field theories (CFTs) of dimension $d>3$, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect's contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on $S^d$ with defect along $S^2$, or on $S^1\times S^{d-1}$ with defect along $S^1\times S^1$. In the latter case we propose that defect central charges appear in an overall normalisation factor, as part of the SUSY Casimir energy. For 2d half-BPS defects in 4d $\mathcal{N}=2$ SCFTs and in the 6d $\mathcal{N}=(2,0)$ SCFT we obtain novel, exact results for defect central charges using existing results for partition functions computed using SUSY localisation, SUSY indices, and correspondences to 2d Liouville, Toda, and $q$-deformed Yang-Mills theories. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large-$N$ and/or strong-coupling limits, but are exact. Our methods can be straightforwardly extended to other superconformal defects, of various codimension, as we demonstrate for a 4d defect in the 6d $\mathcal{N}=(2,0)$ SCFT.

arXiv comment40 pages + 2 appendices, 2 PDF figures; v2 minor clarifications, added references, version published in JHEP

References in corpus (106)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• An Index for 4 dimensional Super Conformal Theories
• On Renormalization Group Flows in Four Dimensions
• Infinite Chiral Symmetry in Four Dimensions
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Reading between the lines of four-dimensional gauge theories
• Two and three-point functions in Liouville theory
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Knot Invariants and Topological Strings
• A finite entanglement entropy and the c-theorem
• On the RG running of the entanglement entropy of a circle
• Holography and Defect Conformal Field Theories
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Gauge Theories and Macdonald Polynomials
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Exact Results in D=2 Supersymmetric Gauge Theories
• Vortex Counting and Lagrangian 3-manifolds
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• The Constraints of Conformal Symmetry on RG Flows
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• On D=5 super Yang-Mills theory and (2,0) theory
• Bootstrapping the superconformal index with surface defects
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• M5-branes from gauge theories on the 5-sphere
• Tinkertoys for Gaiotto Duality
• Cardy Formulae for SUSY Theories in d=4 and d=6
• W Symmetry in six dimensions
• Gauge Theory Loop Operators and Liouville Theory
• Entanglement Entropy, Trace Anomalies and Holography
• 2d Index and Surface operators
• Vertex operator algebras, Higgs branches, and modular differential equations
• Localization on Hopf surfaces
• A Constraint on Defect and Boundary Renormalization Group Flows
• Boundary Conformal Field Theory and a Boundary Central Charge
• Correlation functions in conformal Toda field theory I
• Defects and Quantum Seiberg-Witten Geometry
• Markov property of the CFT vacuum and the a-theorem
• Surface Operators in N=2 4d Gauge Theories
• The g-theorem and quantum information theory
• Affine SL(2) conformal blocks from 4d gauge theories
• A & B model approaches to surface operators and Toda theories
• Interface Yang-Mills, Supersymmetry, and Janus
• Correlation functions in conformal Toda field theory II
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
• Chiral algebras of class S
• Instanton counting with a surface operator and the chain-saw quiver
• Towards a $C$-theorem in defect CFT
• Probing N=4 SYM With Surface Operators
• Supersymmetric Renyi Entropy
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• On Holographic Defect Entropy
• Surface Defects and Chiral Algebras
• Supersymmetric Janus Solutions in Four Dimensions
• Six-Dimensional Tensionless Strings In The Large N Limit
• Universal RG Flows Across Dimensions and Holography
• Vertices, Vortices & Interacting Surface Operators
• M2-brane surface operators and gauge theory dualities in Toda
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Holographic Multiverse
• Displacement Operators and Constraints on Boundary Central Charges
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Weyl anomaly for Wilson surfaces
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Boundary terms of conformal anomaly
• Surface Operators and Separation of Variables
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• Irreversibility in quantum field theories with boundaries
• The Superconformal Index of the (2,0) Theory with Defects
• Conformal anomalies of CFT's with boundaries
• The superconformal index and an elliptic algebra of surface defects
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
• The Liouville side of the Vortex
• Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional
• Intersecting Surface Defects and Two-Dimensional CFT
• Intersecting Surface Defects and Instanton Partition Functions
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• Surface defects and instanton-vortex interaction
• Surface defects, the superconformal index and q-deformed Yang-Mills
• Holographic entanglement entropy from probe M-theory branes
• Holographic multiverse and conformal invariance
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Conformal anomaly of Wilson surface observables - a field theoretical computation
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory
• Marginal deformations and defect anomalies
• On the Weyl anomaly of Wilson surfaces
• Modular and duality properties of surface operators in N=2* gauge theories
• How a-type anomalies can depend on marginal couplings
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• First order formalism for the holographic duals of defect CFTs
• Holographic entanglement entropy of surface defects
• Surface operators in N=2 SQCD and Seiberg Duality
• Analyticity Properties of Graham-Witten Anomalies
• Flavor from M5-branes
• Defect CFTs and holographic multiverse
• The Euler anomaly and scale factors in Liouville/Toda CFTs

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• Surface Defect, Anomalies and $b$-Extremization
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Broken global symmetries and defect conformal manifolds
• Defect $a$-Theorem and $a$-Maximization
• Monodromy Defects in Free Field Theories
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Free energy and defect $C$-theorem in free scalar theory
• A precision test of averaging in AdS/CFT
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Boundary entropy under ambient RG flow in the AdS/BCFT model
• Janus on the Brane
• Observations on BPS observables in 6d
• M2-doughnuts
• Ironing out the crease
• Holographic Generalised Gukov-Witten Defects
• Interface Conformal Anomalies
• BPS surface operators and calibrations
• Surface Operators in Superspace
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy
• Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling