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Phys. Rev. Lett. 81, 2862–2865 (1998)

Theta Dependence in the Large N Limit of Four-Dimensional Gauge Theories

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Edward Witten
School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540

Received 20 July 1998; published in the issue dated 5 October 1998

The θ dependence of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every θ, there are infinitely many vacua that are stable in the large N limit. The true vacuum, found by minimizing the energy in this family, is a smooth function of θ except at θ = π where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped six-branes.

© 1998 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.81.2862
DOI:
10.1103/PhysRevLett.81.2862
PACS:
11.15.Pg, 11.25.Hf, 12.38.Aw