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Non-Abelian statistics versus the Witten anomaly
Published 2012“…We argue that a single Majorana zero mode of the monopole is not compatible with cancellation of the Witten SU(2) anomaly. We also compare this approach with other attempts to realize deconfined non-Abelian objects in 3+1 dimensions.…”
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Schur Times Schubert via the Fomin-Kirillov Algebra
Published 2014“…This approach works in the more general setup of the (small) quantum cohomology ring of the complex flag manifold and the corresponding (3-point) Gromov-Witten invariants. We provide an algebro-combinatorial proof of the nonnegativity of the Gromov-Witten invariants in these cases, and present combinatorial expressions for these coefficients.…”
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Unified formalism for calculating polarization, magnetization, and more in a periodic insulator
Published 2012“…This observation directly leads to the result that the coefficient of the θ term in any dimensions is given by a Wess-Zumino-Witten–type term, integrated in the extended space, interpolating between the original physical Brillouin zone and a trivial system, with the group element replaced by the Green's function. …”
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Jet physics from static charges in AdS space
Published 2012“…We also discuss the linear growth of the charges’ imaginary potential energy with separation, and a relationship between Wilson line diagrams and Witten diagrams.…”
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New monotonicity formulas for Ricci curvature and applications; I
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Symmetry-Protected Quantum Spin Hall Phases in Two Dimensions
Published 2013“…At an open boundary, the θ term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. …”
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Majorana zero-modes and topological phases of multi-flavored Jackiw-Rebbi model
Published 2014“…Our results also indicate that a single normalizable Majorana zero mode can be compatible with the cancellation of SU(2) Witten anomaly.…”
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Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
Published 2012“…The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. …”
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Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders
Published 2013“…We refer to other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as non-ABJ gauge anomalies, which include Witten SU(2) global gauge anomalies. We introduce a notion of π-cohomology group, H[-d+1 over π](BG,R/Z), for the classifying space BG, which is an Abelian group and include Tor[H[superscript d+1](G,R/Z)] and topological cohomology group H[superscript d+1](BG,R/Z) as subgroups. …”
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Symmetry-protected topological phases with charge and spin symmetries: Response theory and dynamical gauge theory in two and three dimensions
Published 2014“…For the SPT examples we consider {i.e., U[subscript c](1)⋊Z[T over 2], U[subscript s](1)×Z[T over 2], U[subscript c](1)×[U[subscript s](1)⋊Z[subscript 2]]; subscripts c and s are short for charge and spin; Z[T over 2] and Z[subscript 2] are time-reversal symmetry and π rotation about S[subscript y], respectively}, many variants of Witten effect in the 3D SPT bulk and various versions of anomalous surface quantum Hall effect are defined and systematically investigated. …”
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Symmetry protected topological orders and the group cohomology of their symmetry group
Published 2014“…The boundary excitations of the nontrivial SPT phases are described by lattice nonlinear σ models with a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear σ models. As a result, the symmetry G must be realized as a non-on-site symmetry for the low-energy boundary excitations, and those boundary states must be gapless or degenerate. …”
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