Theta Dependence in the Large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">N</mml:mi></mml:math>Limit of Four-Dimensional Gauge Theories

The theta dependent 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 theta, 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 theta except at theta equal to pi, where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped sixbranes.