English

Eta-Invariants and Determinant Lines

High Energy Physics - Theory 2016-09-06 v4 dg-ga Differential Geometry

Abstract

We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We prove a gluing law and a variation formula for this invariant. This yields a new, simpler proof of the holonomy formula for the determinant line bundle of a family of Dirac operators, also known as the ``global anomaly'' formula. This paper is written using AMSTeX 2.1, which can be obtained via ftp from the American Mathematical Society (instructions included). A postscript file with figures was submitted separately in uuencoded tar-compressed format.

Keywords

Cite

@article{arxiv.hep-th/9405012,
  title  = {Eta-Invariants and Determinant Lines},
  author = {Xianzhe Dai and Daniel S. Freed},
  journal= {arXiv preprint arXiv:hep-th/9405012},
  year   = {2016}
}

Comments

53 pages + 3 figures (added historical references, made a few minor writing corrections)

R2 v1 2026-07-22T15:49:51.388Z