Wed·Sep 26, 2007Wednesday·September 26, 2007

1. 01*

   The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

   P. K. Mitter🇫🇷 · B. Scoppola🇮🇹

   We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric ${\Phi }^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) Lévy random walk in $Z^3$. The Green's function depends on the Lévy-Khintchine parameter $\alpha =\frac{3+ϵ}{2}$ with $0<\alpha <2$. For $\alpha =\frac{3}{2}$ the ${\Phi }^4$ interaction is marginal. We prove for $\alpha -\frac{3}{2}=\frac{ϵ}{2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding Lévy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding Lévy walk in $Z^3$.

   ↳ math-phhep-lathep-thmath.MPJ.Statist.Phys.(2008)·12 citations
2. 02*

   Rho meson condensation at finite isospin chemical potential in a holographic model for QCD

   Ofer Aharony🇮🇱 · Kasper Peeters🇳🇱 · Jacob Sonnenschein🇮🇱 · Marija Zamaklar🇬🇧

   We analyze the effect of an isospin chemical potential \mu_I in the Sakai-Sugimoto model, which is the string dual of a confining gauge theory related to large N_c QCD, at temperatures below the chiral symmetry restoration temperature. For small chemical potentials we show that the results agree with expectations from the low-energy chiral Lagrangian, and the charged pion condenses. When the chemical potential reaches a critical value \mu_I = \mu_{crit} ~ 1.7 m_{\rho}, the lowest vector meson (the "rho meson") becomes massless, and it condenses (in addition to the pion condensate) for \mu_I > \mu_{crit}. This spontaneously breaks the rotational symmetry, as well as a residual U(1) flavor symmetry. We numerically construct the resulting new ground state for \mu_I > \mu_{crit}.

   ↳ hep-thhep-lathep-phJHEP(2008)·106 citations
3. 03*

   Two-Point Functions of Coulomb Gauge Yang-Mills Theory

   Peter Watson🇩🇪 · Hugo Reinhardt🇩🇪

   The functional approach to Coulomb gauge Yang-Mills theory is considered within the standard, second order, formalism. The Dyson-Schwinger equations and Slavnov-Taylor identities concerning the two-point functions are derived explicitly and one-loop perturbative results are presented.

   ↳ hep-thhep-lathep-phPRD(2008)·58 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.