- 日時 ： 12月11日（火） 午後１時３０分~
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場所 ：理学部Ｆ棟５階 理論物質学セミナー室（Ｆ５２４）
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講演者 ：深谷 英則 氏（阪大理・物理）
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タイトル: "Atiyah-Patodi-Singer index theorem and topological matters"
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概要 ：
The Atiyah-Patodi-Singer(APS) index theorem attracts attention for
understanding physics on the surface of materials in topological
phases. The mathematical set-up for this theorem is, however, not
directly related to the physical fermion system, as it imposes on the
fermion fields a non-local boundary condition known as the "APS
boundary condition" by hand, which is unlikely to be realized in the
materials. In this work, we attempt to reformulate the APS index in a
"physicist-friendly" way for a simple set-up with U(1) or SU(N) gauge
group on a flat four-dimensional Euclidean space. We find that the
same index as APS is obtained from the domain-wall fermion Dirac
operator with a local boundary condition, which is naturally given by
the kink structure in the mass term. As the boundary condition does
not depend on the gauge fields, our new definition of the index is
easy to compute with the standard Fujikawa method. This talk is based
on HF, Tetsuya Onogi, and Satoshi Yamaguchi, Phys.Rev. D96 (2017)
no.12, 125004 [arXiv:1710.03379].