The Role of Vortex Strings in the Non-Compact Lattice Abelian Higgs Model

The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant ``vortex'' strings. The phase transition of the system is then related to the density of these excitations. Through Monte Carlo simulations the density of the vortex sheets is shown to be a good order parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate.Comment: 11 pages LaTeX2e, 4 Postscript figures, uses epsf.sty, references adde

Submanifolds, Isoperimetric Inequalities and Optimal Transportation

The aim of this paper is to prove isoperimetric inequalities on submanifolds of the Euclidean space using mass transportation methods. We obtain a sharp ?weighted isoperimetric inequality? and a nonsharp classical inequality similar to the one obtained by J. Michael and L. Simon. The proof relies on the description of a solution of the problem of Monge when the initial measure is supported in a submanifold and the final one supported in a linear subspace of the same dimension

Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant Four-Fermion Interactions

Lattice QCD with additional chiral-invariant four-fermion interactions is studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The four-fermion interactions are implemented by introducing bosonic auxiliary fields. A mean field treatment of the auxiliary fields is used to calculate the model's asymptotic scale parameter and perturbative thermodynamics, including the one-loop gluonic contributions to the energy, entropy, and pressure. In this approach the calculations reduce to those of ordinary lattice QCD with massive quarks. Hence, the previous calculations of these quantities in lattice QCD using massless quarks are generalized to the massive case.Comment: 22 pages, RevTeX, 8 EPS figures, uses epsf.sty and feynmf.st

Multiple Signals Converge on a Differentiation MAPK Pathway

An important emerging question in the area of signal transduction is how information from different pathways becomes integrated into a highly coordinated response. In budding yeast, multiple pathways regulate filamentous growth, a complex differentiation response that occurs under specific environmental conditions. To identify new aspects of filamentous growth regulation, we used a novel screening approach (called secretion profiling) that measures release of the extracellular domain of Msb2p, the signaling mucin which functions at the head of the filamentous growth (FG) MAPK pathway. Secretion profiling of complementary genomic collections showed that many of the pathways that regulate filamentous growth (RAS, RIM101, OPI1, and RTG) were also required for FG pathway activation. This regulation sensitized the FG pathway to multiple stimuli and synchronized it to the global signaling network. Several of the regulators were required for MSB2 expression, which identifies the MSB2 promoter as a target “hub” where multiple signals converge. Accessibility to the MSB2 promoter was further regulated by the histone deacetylase (HDAC) Rpd3p(L), which positively regulated FG pathway activity and filamentous growth. Our findings provide the first glimpse of a global regulatory hierarchy among the pathways that control filamentous growth. Systems-level integration of signaling circuitry is likely to coordinate other regulatory networks that control complex behaviors

Phase transitions in lattice gauge theories

Topological excitations in lattice gauge theories are studied with an aim towards understanding the role of such excitations in the Abelian Higgs model. First, the topological excitations of the compact U(l) lattice Higgs model are reviewed. The phases of the system are discussed in terms of these excitations and the results of Monte Carlo studies summarized. New results are then presented clarifying the role of topological excitations in the non-compact lattice version of the Abelian Higgs model. The Villain form of the non-compact model's partition function is represented as a sum over world-sheets of gauge-invariant "vortex" sheets. The phase transition of the system is then related to the condensation of these excitations via standard energy-entropy arguments. Results of Monte Carlo simulations are then presented. The density of the vortex sheets is shown to be a good disorder parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate. The critical line derived in the vortex representation of the theory is in good agreement with the Monte Carlo results. In part II Quantum Chromo dynamics ( QCD) is studied at non-zero baryon density. The essential properties of QCD are reviewed, including the broken chiral symmetry of the QCD vacuum state. The current understanding of the deconfining and chiral symmetry restoring transitions at non-zero temperature and density is then summarized. The use of a four-fermion coupling as an improved extrapolation parameter over the bare quark mass in Monte Carlo simulations is discussed. A mean field analysis of finite density QCD is then presented, including the effects of additional chiral invariant four-fermion interactions. A lattice regularization is used with N1 = 4 flavors of staggered fermions. Particular attention is given to the structure of the phase diagram and the order of the chiral phase transition. At zero gauge coupling the model reduces to a Nambu-Jona-Lasinio model. In this limit the chiral phase transition is found to be second-order near the zero-density critical point and otherwise first-order. In the strong gauge coupling limit a first-order chiral phase transition is found. In this limit the additional four-fermion interactions do not qualitatively change the physics. The results agree with previous studies of QCD as the four-fermion coupling vanishes.U of I OnlyThesi

The geometric triharmonic heat flow of immersed surfaces near spheres

We consider closed immersed surfaces in R^3 evolving by the geometric triharmonic heat flow. Using local energy estimates, we prove interior estimates and a positive absolute lower bound on the lifespan of solutions depending solely on the local concentration of curvature of the initial immersion in L^2. We further use an {\epsilon}-regularity type result to prove a gap lemma for stationary solutions. Using a monotonicity argument, we then prove that a blowup of the flow approaching a singular time is asymptotic to a non-umbilic embedded stationary surface. This allows us to conclude that any solution with initial L^2-norm of the tracefree curvature tensor smaller than an absolute positive constant converges exponentially fast to a round sphere with radius equal to the cube root of 3V_0/4{\pi}, where V_0 denotes the signed enclosed volume of the initial data