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Necessary and sufficient conditions for the validity of Luttinger’s theorem
Published 2020-01-01“…In this paper, we propose the minimal requirements for the application of a hard Luttinger’s theorem to a generic fermionic system of arbitrary interaction strength by invoking the Atiyah–Singer index theorem to quantify the topologically-robust behavior of a generalized Fermi surface. …”
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Index theorems and magnetic monopoles on asymptotically conic manifolds
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Verification & discretization of the index theorem for a two dimensional dirac operator
Published 2015“…The famous Atiyah-Singer Index Theorem states that for an elliptic partial differential operator D on a compact manifold, the analytical index (related to the solution space of the partial differential equation Df = 0) is equal to the topological index (defined in terms of some topological data of D). …”
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Gravitational anomalies of fermionic higher-spin fields
Published 2022-09-01“…Abstract Using the Atiyah-Singer index theorem, we formally compute gravitational anomalies for fermionic higher-spin fields in two, six and ten dimensions, as well as the U(1) mixed gauge-gravitational anomaly in four dimensions. …”
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Influence of topology on fermionic zero-modes in lattice gauge theory
Published 2010“…The staggered fermion index obtained is shown to be determined by the underlying gauge field topology in accordance with the Atiyah-Singer Index theorem. It is also found to perform as well as the Wilson index, while being computationally more efficient.…”
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Index of lattice dirac operators
Published 2014“…The general topic of this thesis is how to define and compute the index of discretised “lattice” versions of the Dirac operator coupled to a topologically nontrivial gauge field. The famous Atiyah-Singer Index Theorem, applied to the usual continuum Dirac operator, says that its index is equal to the topological charge of the gauge field. …”
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Anomaly constraints and string/F-theory geometry in 6D quantum gravity
Published 2019“…Quantum anomalies, determined by the Atiyah-Singer in- dex theorem, place strong constraints on the space of quantu m gravity theories in six dimensions with minimal supersymmetry. …”
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