Fusion of conformal interfaces

Abstract

We study the fusion of conformal interfaces in the c=1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological interfaces, which (a) minimize the entropy function, (b) fix through an attractor mechanism one or both of the bulk radii, and (c) are (marginally) stable under splitting. One significant difference is that the conserved charges are logarithms of natural numbers, rather than vectors in a charge lattice, as for BPS states. Besides potential applications to condensed-matter physics and number theory, these results point to the existence of large solution-generating algebras in string theory.

28 pages, 4 figures. Minor clarifications in v2. Sign Mistakes corrected and reference added in v3

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Cited by in corpus (73)

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• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• Entanglement through conformal interfaces
• Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface conformal field theories
• A worldsheet extension of O(d,d;Z)
• Energy Reflection and Transmission at 2D Holographic Interfaces
• Invertible defects and isomorphisms of rational CFTs
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Lorentzian Dynamics and Factorization Beyond Rationality
• Phases of Holographic Interfaces
• Non-Equilibrium Conformal Field Theories with Impurities
• Defect flows in minimal models
• Entanglement entropy at holographic interfaces
• Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant
• Defect loops in gauged Wess-Zumino-Witten models
• 't Hooft Operators in Gauge Theory from Toda CFT
• Entanglement entropy at CFT junctions
• More on Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant
• Energy Transport for Thick Holographic Branes
• RG boundaries and interfaces in Ising field theory
• Entanglement and topological interfaces
• Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Some remarks on defects and T-duality
• Universal relations for holographic interfaces
• Steady States of Holographic Interfaces
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Defects and Permutation branes in the Liouville field theory
• String Junctions and Holographic Interfaces
• A note on entanglement entropy for topological interfaces in RCFTs
• Calabi's diastasis as interface entropy
• On the Symmetries of Classical String Theory
• Conformal Janus on Euclidean Sphere
• Superconformal defects in the tricritical Ising model
• Boundary RG Flows for Fermions and the Mod 2 Anomaly
• Fusion of conformal defects in four dimensions
• Lie algebra lattices and strings on T-folds
• Marginal quenches and drives in Tomonaga-Luttinger liquids
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
• Defect Perturbations in Landau-Ginzburg Models
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
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• Realizing IR theories by projections in the UV
• Holographic Weak Measurement
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• Holographic Entropy and Calabi's Diastasis
• Topological interfaces in Chern-Simons theory and $Ad{S}_3/CF{T}_2$
• Gerbe-holonomy for surfaces with defect networks
• Phase transitions in GLSMs and defects
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• Modular Orbits at Higher Genus
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• Topological defects in string theory orbifolds with target spaces $\mathbb{C}/{\mathbb{Z}}_N$ and $S^1/{\mathbb{Z}}_2$