Minimal subtraction and the Callan-Symanzik equation

The usual proof of renormalizability using the Callan-Symanzik equation makes explicit use of normalization conditions. It is shown that demanding that the renormalization group functions take the form required for minimal subtraction allows one to prove renormalizability using the Callan-Symanzik equation, without imposing normalization conditions. Scalar field theory and quantum electrodynamics are treated.Comment: 6 pages, plain Te

A Gradient Flow for Worldsheet Nonlinear Sigma Models

We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a Riemannian metric, dilaton, and 2-form B-field. By generalizing recent mathematical results to incorporate the B-field and by decoupling the dilaton, we are able to describe the 1-loop beta-functions of the metric and B-field as the components of the gradient of a potential functional on the space of coupling constants. We emphasize a special choice of diffeomorphism gauge generated by the lowest eigenfunction of a certain Schrodinger operator whose potential and kinetic terms evolve along the flow. With this choice, the potential functional is the corresponding lowest eigenvalue, and gives the order alpha' correction to the Weyl anomaly at fixed points of (g(t),B(t)). Since the lowest eigenvalue is monotonic along the flow and reproduces the Weyl anomaly at fixed points, it accords with the c-theorem for flows that remain always in the first-order regime. We compute the Hessian of the lowest eigenvalue functional and use it to discuss the linear stability of points where the 1-loop beta-functions vanish, such as flat tori and K3 manifolds.Comment: Accepted version for publication. Citations added to Friedan and to Fateev, Onofri, and Zamolodchikov. Introduction modified slightly to discuss these citations. 25 pages, LaTe

A Nonperturbative Calculation of Basic Chiral QCD Parameters Within Zero Modes Enhancement Model of the QCD Vacuum. I

A new zero modes enhancement (ZME) model of the true QCD vacuum is breifly described. It makes possible to analytically investigate and calculate numerically low-energy QCD structure from first principles. Expressions of basic chiral QCD parameters (the pion decay constant, the quark and gluon condensates, the dynamically generated quark mass, etc) as well as the vacuum energy density (up to the sign, by definition, the bag constant), suitable for numerical calculations, have been derived. Solution to the Schwinger-Dyson (SD) equation for the quark propagator in the infrared (IR) domain on the basis of the ZME effect in QCD was used for this purpose. There are only two independent quantities (free parameters) by means of which calculations must be done within our approach. The first one is the integration constant of the above mentioned quark SD equation of motion. The second one is a scale at which nonperturbative effects begin to play a dominant role.Comment: 17 pages, two figures added, minor change

Phase Transition Couplings in U(1) and SU(N) Regularized Gauge Theories

Using a 2-loop approximation for $\beta$-functions, we have considered the corresponding renormalization group improved effective potential in the Dual Abelian Higgs Model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU(N) regularized gauge theories. In contrast to our previous result $\alpha_{crit} \approx 0.17$, obtained in the one-loop approximation with the DAHM effective potential (see Ref.[20]), the critical value of the electric fine structure constant in the 2-loop approximation, calculated in the present paper, is equal to $\alpha_{crit}\approx 0.208$ and coincides with the lattice result for compact QED [10]: $\alpha_{crit}^{lat} \approx 0.20\pm 0.015$. Following the 't Hooft's idea of the "abelization" of monopole vacuum in the Yang--Mills theories, we have obtained an estimation of the SU(N) triple point coupling constants, which is $\alpha_{N,crit}^{-1}=\frac{N}{2}\sqrt{\frac{N+1}{N-1}} \alpha_{U(1),crit}^{-1}$. This relation was used for the description of the Planck scale values of the inverse running constants $\alpha_i^{-1}(\mu)$ (i=1,2,3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the Multiple Point Model [16].Comment: 24 pages, 3 figure

One-Loop Renormalization of Lorentz-Violating Electrodynamics

We show that the general Lorentz- and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The one-loop Lorentz-violating beta functions are obtained, and the running of the coefficients for Lorentz and CPT violation is determined. Some implications for theory and experiment are discussed.Comment: 12 pages, accepted for publication in Physical Review

Multibaryons as Symmetric Multiskyrmions

We study non-adiabatic corrections to multibaryon systems within the bound state approach to the SU(3) Skyrme model. We use approximate ansatze for the static background fields based on rational maps which have the same symmetries of the exact solutions. To determine the explicit form of the collective Hamiltonians and wave functions we only make use of these symmetries. Thus, the expressions obtained are also valid in the exact case. On the other hand, the inertia parameters and hyperfine splitting constants we calculate do depend on the detailed form of the ansatze and are, therefore, approximate. Using these values we compute the low lying spectra of multibaryons with B <= 9 and strangeness 0, -1 and -B. Finally, we show that the non-adiabatic corrections do not affect the stability of the tetralambda and heptalambda found in a previous work.Comment: 17 pages, RevTeX, no figure

Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at N_c->oo), with the emphasis on the spectator-dependent effects sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the `t Hooft equation. We show that the 1/m_Q expansion of both the Weak Annihilation and Pauli Interference widths coincides with the OPE predictions, to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the 1/m_Q expansion in the 't~Hooft model.Comment: 54 pages, 8 figures in the text. Version to be published in Phys. Rev. D. A number of typos are corrected and relevant references added. Clarifications in Conclusions, Appendices 2.1 and 3 are adde

Gribov Problem for Gauge Theories: a Pedagogical Introduction

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear differential equation, and the various solutions of such a non-linear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.Comment: 24 pages, Revtex 4. In the revised version, a statement has been amended on page 11, and References 14, 16 and 27 have been improve

Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement

We give an outline of a recent proof that the low-energy effective gauge theory exhibiting quark confinement due to magnetic monopole condensation can be derived from QCD without any specific assumption. We emphasize that the low-energy effective abelian gauge theories obtained here give the dual description of the same physics in the low-energy region. They show that the QCD vacuum is nothing but the dual (type II) superconductor.Comment: 15 pages, Latex, no figures, Talk given at YKIS'97, Non-perturbative QCD, Kyot

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps