Quantum phase transitions in cascading gauge theory

We study a ground state of N=1 supersymmetric SU(K+P) x SU(K) cascading gauge theory of Klebanov et.al [1,2] on R x S^3 at zero temperature. A radius of S^3 sets a compactification scale mu. An interplay between mu and the strong coupling scale Lambda of the theory leads to an interesting pattern of quantum phases of the system. For mu > mu_cSB=1.240467(8)Lambda the ground state of the theory is chirally symmetric. At mu=mu_cSB the theory undergoes the first-order transition to a phase with spontaneous breaking of the chiral symmetry. We further demonstrate that the chirally symmetric ground state of cascading gauge theory becomes perturbatively unstable at scales below mu_c=0.950634(5)mu_cSB. Finally, we point out that for mu < 1.486402(5)Lambda the stress-energy tensor of cascading gauge theory can source inflation of a closed Universe.Comment: 62 pages, 9 figure

Mass Spectrum and Bounds on the Couplings in Yukawa Models With Mirror-Fermions

The $\rm SU(2)_L\otimes SU(2)_R$ symmetric Yukawa model with mirror-fermions in the limit where the mirror-fermion is decoupled is studied both analytically and numerically. The bare scalar self-coupling $\lambda$ is fixed at zero and infinity. The phase structure is explored and the relevant phase transition is found to be consistent with a second order one. The fermionic mass spectrum close to that transition is discussed and a first non-perturbative estimate of the influence of fermions on the upper and lower bounds on the renormalized scalar self-coupling is given. Numerical results are confronted with perturbative predictions.Comment: 7 (Latex) page

Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background

We investigate the one-loop energy shift E to certain two-impurity string states in light-cone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers which cancel between the cubic Hamiltonian and quartic ``contact term''. Analyzing the impurity non-conserving channel we find that the non-perturbative, order g_2^2 sqrt(lambda') contribution to E/mu predicted in hep-th/0211220 is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an order g_2^2 lambda' contribution. Exploiting the supersymmetry algebra, we present a form for the energy shift which appears to be manifestly convergent and free of non-perturbative terms. We use this form to argue that E/mu receives order g_2^2 lambda' contributions at every order in intermediate state impurities.Comment: 27 pages; added references, acknowledgments, missing normalization in equations 2.3 - 2.8, also cleaned up notation, and added a few footnote

Formal analytical solutions for the Gross-Pitaevskii equation

Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ as a function of a unique dimensionless non-linear parameter $\Lambda$. We report solutions for different range of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of $\Lambda$. Introducing an accumulated error function we have performed a quantitative analysis with other well-established methods as: the perturbation theory, the Thomas-Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the $\Lambda$-values where each solution can be easily implemented. In particular we showed that for $\Lambda <-9$, the bright soliton function reproduces the exact solution of GPE wave function.Comment: 8 figure