QCD at theta similar to pi reexamined: Domain walls and spontaneous CP violation - art. no. 114009

We consider QCD at theta similar to pi with two, one and zero light flavors N-f, using the Di Vecchia-Veneziano-Witten effective Lagrangian. For N-f=2 , we show that CP is spontaneously broken at theta=pi for finite quark mass splittings, z=m(d)/m(u)not equal 1. In the z - theta plane, there is a lin e of first order transitions at theta=pi with two critical end points, z(1) *<z<z(2)*. We compute the tension of the domain walls that relate the two C P violating vacua. For m(u) = m(d), the tension of the family of equivalent domain walls agrees with the expression derived by Smilga from chiral pert urbation theory at next-to-leading order. For z(1)*<z<z(2)*, z not equal 1, there is only one domain wall and a wall-some sphaleron at theta=pi. At th e critical points, z=z(1,2)* the domain wall fades away, CP is restored and the transition becomes of second order. For N-f=1, CP is spontaneously bro ken only if the number of colors N-c is large and/or if the quark is suffic iently heavy. Taking the heavy quark limit (similar to N-f =0) provides a s imple derivation of the multibranch theta dependence of the vacuum energy o f large N-c pure Yang-Mills theory. In the large N-c limit, there are many quasistable vacua with a decay rate Gamma similar to exp(-N-c(4)).