Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
Surface Defects and Chiral Algebras
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abstract
We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.
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Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
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Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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Generalised 4d Partition Functions and Modular Differential Equations
Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
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Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
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When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.