Cascading gauge theory on dS_4 and String Theory Landscape

Placing anti-D3 branes at the tip of the conifold in Klebanov-Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e, there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes.Comment: 47 pages, 6 figures. v2: published version. arXiv admin note: substantial text overlap with arXiv:1108.607

Theta-vacuum: Phase Transitions and/or Symmetry Breaking at θ=π\theta = \pi

Assuming that a quantum field theory with a $\theta$-vacuum term in the action shows non-trivial $\theta$-dependence and provided that some reasonable properties of the probability distribution function of the order parameter hold, we argue that the theory either breaks spontaneously CP at $\theta = \pi$ or shows a singular behavior at some critical $\theta_c$ between 0 and $\pi$. This result, which applies to any model with a pure imaginary contribution to the euclidean action consisting in a quantized charge coupled to a phase, as QCD, is illustrated with two simple examples; one of them intimately related to Witten's result on SU(N) in the large $N$ limit.Comment: 9 pages, 2 figures, 2 references added, final version to appear in Progr. Theor. Phy

QCD with a theta-vacuum term: a complex system with a simple complex action

We reanalyze in the first part of this paper the old question of P and CT realization in QCD. The second part is devoted to establish general results on the phase structure of this model in the presence of a $\theta$-vacuum term.Comment: 15 pages, to be published in the proceedings of the ``International Workshop on Non-Perturbative Methods and Lattice QCD'', Guangzhou, China, 15-21 May 200