Introduces subdimensional entanglement entropy (SEE) as a probe of geometric-topological responses in quantum phases and establishes a bulk-to-mixed-state holographic correspondence via strong and weak symmetries on subdimensional subsystems.
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Gravitational Anomalies and Thermal Hall effect in Topological Insulators
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It has been suggested that a temperature gradient will induce a Leduc-Righi, or thermal Hall, current in the Majorana quasiparticles localized on the surface of class DIII topological insulators, and that the magnitude of this current can be related {\it via} an Einstein argument to a Hall-like energy flux induced by gravity. We critically examine this idea, and argue that the gravitational Hall effect is more complicated than its familiar analogue. A conventional Hall current is generated by a {\it uniform} electric field, but computing the flux from the gravitational Chern-Simons functional shows that gravitational field {\it gradients} - i.e. tidal forces - are needed to induce a energy-momentum flow. We relate the surface energy-momentum flux to a domain-wall gravitational anomaly {\it via} the Callan-Harvey inflow mechanism. We stress that the gauge invariance of the combined bulk-plus-boundary theory ensures that the current in the domain wall always experiences a "covariant" rather than "consistent" anomaly. We use this observation to confirm that the tidally induced energy-momentum current exactly accounts for the covariant gravitational anomaly in $(1+1)$ dimensional domain-wall fermions. The same anomaly arises whether we write the Chern-Simons functional in terms of the Christofflel symbol or in terms of the the spin connection.
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Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
Derives a generic chiral anomaly formula incorporating multiple Feynman diagrams, from which abelian, singlet, consistent, and covariant forms follow, with topological discussion and FeynCalc code.
Framework using smeared boundary CFTs classifies gapped phases dual to massless RG flows, showing they often spontaneously break non-group-like symmetries via unusual module structures outside standard boundary critical phenomena.
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