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Effective field theories for topological insulators via functional bosonization

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Mathematics and Physics of the Holographic Principle

Effective field theories that describes the dynamics of a conserved U(1) current in terms of hydrodynamic degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant, we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative fractional topological insulators and their possible effective field theories, and use them to determine the physical properties of these.

This talk is part of the Isaac Newton Institute Seminar Series series.

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