Free Fermion Symmetry Breaking and a Long Exact Sequence in K-Theory
ORAL
Abstract
We study symmetry breaking for free fermions. Specifically, we show how three processes
(1) producing Jackiw-Rebbi modes on a defect by imposing certain boundary conditions on a charged order parameter,
(2) counting zero modes localized to the origin of a free fermion Berry phase, and
(3) extending a lower-dimensional theory to a higher-dimensional theory with a mass term away from the origin
are mathematically described by Thom isomorphisms and by maps in a long exact sequence in equivariant K-theory. Using this framework, we can examine both the 10-fold way for free electron systems and anomaly matching in the spontaneous symmetry broken phase for more general free fermion phases.
(1) producing Jackiw-Rebbi modes on a defect by imposing certain boundary conditions on a charged order parameter,
(2) counting zero modes localized to the origin of a free fermion Berry phase, and
(3) extending a lower-dimensional theory to a higher-dimensional theory with a mass term away from the origin
are mathematically described by Thom isomorphisms and by maps in a long exact sequence in equivariant K-theory. Using this framework, we can examine both the 10-fold way for free electron systems and anomaly matching in the spontaneous symmetry broken phase for more general free fermion phases.
*This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1122374.
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Presenters
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Cameron Krulewski
- Massachusetts Institute of Technology