New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
TFT construction of RCFT correlators II: Unoriented world sheets
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A full rational CFT, consistent on all orientable world sheets, can be constructed from the underlying chiral CFT, i.e. a vertex algebra, its representation category C, and the system of chiral blocks, once we select a symmetric special Frobenius algebra A in the category C [I]. Here we show that the construction of [I] can be extended to unoriented world sheets by specifying one additional datum: a reversion on A - an isomorphism from the opposed algebra of A to A that squares to the twist. A given full CFT on oriented surfaces can admit inequivalent reversions, which give rise to different amplitudes on unoriented surfaces, in particular to different Klein bottle amplitudes. We study the classification of reversions, work out the construction of the annulus, Moebius strip and Klein bottle partition functions, and discuss properties of defect lines on non-orientable world sheets. As an illustration, the Ising model is treated in detail.
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A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
Derives additivity and fusion rules for defect g-functions in integrable 2D QFT, with effective amplitudes for non-topological cases and lowered entropy contribution in Ising non-topological fusion.
Topological defects constrain the allowed RG flows of N=1 superconformal minimal models, first via a bosonic coset description and then for the full superconformal case.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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From gauging to duality in one-dimensional quantum lattice models
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.