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Hidden Topological Angles in Path Integrals.

Authors
  • Behtash, Alireza1
  • Sulejmanpasic, Tin1
  • Schäfer, Thomas1
  • Ünsal, Mithat1
  • 1 Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.
Type
Published Article
Journal
Physical Review Letters
Publisher
American Physical Society
Publication Date
Jul 24, 2015
Volume
115
Issue
4
Pages
41601–41601
Identifiers
PMID: 26252675
Source
Medline
License
Unknown

Abstract

We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta parameters in the Lagrangian. They arise as invariant angles associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in n_{f} to a noninteger number of flavors, reducing in the integer n_{f} limit to a Z_{2} valued phase difference between dominant saddles. In N=1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like SU(N) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semiclassical expansion. In quantum mechanics, a HTA leads to a difference in semiclassical expansion of integer and half-integer spin particles.

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