2,822 research outputs found
Mixed global anomalies and boundary conformal field theories
We consider the relation of mixed global gauge gravitational anomalies and
boundary conformal field theory in WZW models for simple Lie groups. The
discrete symmetries of consideration are the centers of the simple Lie groups.
These mixed anomalies prevent to gauge them i.e, take the orbifold by the
center. The absence of anomalies impose conditions on the levels of WZW models.
Next, we study the conformal boundary conditions for the original theories. We
consider the existence of a conformal boundary state invariant under the action
of the center. This also gives conditions on the levels of WZW models. By
considering the combined action of the center and charge conjugation on
boundary states, we reproduce the condition obtained in the orbifold analysis.Comment: 24pages, 1 figure, references adde
D-branes on a Noncompact Singular Calabi-Yau Manifold
We investigate D-branes on a noncompact singular Calabi-Yau manifold by using
the boundary CFT description, and calculate the open string Witten indices
between the boundary states. The B-type D-branes turn out to be characterized
by the properties of a compact positively curved manifold. We give geometric
interpretations to these boundary states in terms of coherent sheaves of the
manifold.Comment: 31 pages, LaTeX, 1 figure, amsmath, minor changes, references are
added, a figure is adde
Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for
understanding physics on the surface of materials in topological phases.
Although it is widely applied to physics, the mathematical set-up in the
original APS index theorem is too abstract and general (allowing non-trivial
metric and so on) and also the connection between the APS boundary condition
and the physical boundary condition on the surface of topological material is
unclear. For this reason, in contrast to the Atiyah-Singer index theorem,
derivation of the APS index theorem in physics language is still missing. In
this talk, we attempt to reformulate the APS index in a "physicist-friendly"
way, similar to the Fujikawa method on closed manifolds, for our familiar
domain-wall fermion Dirac operator in a flat Euclidean space. We find that the
APS index is naturally embedded in the determinant of domain-wall fermions,
representing the so-called anomaly descent equations.Comment: 8 pages, Proceedings of the 35th annual International Symposium on
Lattice Field Theor
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