1+1 dimensional QCD with fundamental bosons and fermions

We analyze the properties of mesons in 1+1 dimensional QCD with bosonic and fermionic ``quarks'' in the large \nc limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of ``mesons'' formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.Comment: 20 pages, harvmac, 5 figure

Sigma model approach to string theory effective actions with tachyons

Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within sigma model approach. In particular, we demonstrate that the renormalized partition function $Z(T,A)$ of boundary sigma model gives the effective action for massless vectors which is consistent with string S-matrix and beta function, resolving an old problem with this suggestion in bosonic string case at the level of the leading $F^2 (dF)^2$ derivative corrections to Born-Infeld action. We give manifestly gauge invariant definition of $Z(T,A)$ in non-abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories.Comment: 26 pages, harvmac. To appear in the special issue of J. Math. Phys. on Strings, Branes and M-theory. v4: minor editorial changes, version to appear in JM

The Standard Model with gravity couplings

In this paper, we examine the coupling of matter fields to gravity within the framework of the Standard Model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti)self-dual or left-handed spin connection fields. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C and T; and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.Comment: Extended, and replaced with LaTex file. 25 Page

Bounding Anomalous Gauge-Boson Couplings

In this version we have corrected some minor errors in the tables, corrected typos, and added a reference. We have also updated our comparison with earlier workers. Figures are now included as uuencoded compressed tar files.Comment: 32 page

Decay of Metastable Topological Defects

We systematically analyze the decay of metastable topological defects that arise from the spontaneous breakdown of gauge or global symmetries. Quantum-mechanical tunneling rates are estimated for a variety of decay processes. The decay rate for a global string, vortex, domain wall, or kink is typically suppressed compared to the decay rate for its gauged counterpart. We also discuss the decay of global texture, and of semilocal and electroweak strings.Comment: 43 pages, harvmac, HUTP-92/A018, CALT-68-178

Charge Radii and Magnetic Polarizabilities of the Rho and K* Mesons in QCD String Theory

The effective action for light mesons in the external uniform static electromagnetic fields was obtained on the basis of QCD string theory. We imply that in the presence of light quarks the area law of the Wilson loop integral is valid. The approximation of the Nambu-Goto straight-line string is used to simplify the problem. The Coulomb-like short-range contribution which goes from one-gluon exchange is also neglected. We do not take into account spin-orbital and spin-spin interactions of quarks and observe the $\rho$ and $K^*$ mesons. The wave function of the meson ground state is the Airy function. Using the virial theorem we estimate the mean charge radii of mesons in terms of the string tension and the Airy function zero. On the basis of the perturbative theory, in the small external magnetic field we find the diamagnetic polarizabilities of $\rho$ and $K^*$ mesons: $\beta_\rho =-0.8\times 10^{-4} {fm}^3$, $\beta_{K^*}=-0.57\times 10^{-4} {fm}^3$Comment: 22 pages, no figures, in LaTeX 2.09, typos correcte

Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking

We investigate in some detail a "variational mass" expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the $SU(2)_L \times SU(2)_R$ and $SU(3)_L \times SU(3)_R$ chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass $m$. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in $m$ properties. In the approximation where the explicit breakdown of the chiral symmetries due to small current quark masses is neglected, we derive ansatzes for the dynamical contribution to the "constituent" masses $M_q$ of the $u,d,s$ quarks; the pion decay constant $F_\pi$; and the quark condensate $$ in terms of the basic QCD scale $\Lambda_{\bar{MS}}$. Those ansatzes are then optimized, in a sense to be specified, and also explicit symmetry breaking mass terms can be consistently introduced in the framework. The obtained values of $F_\pi$ and $M_q$ are roughly in agreement with what is expected from other non-perturbative methods. In contrast we obtain quite a small value of $|< \bar q q >|$ within our approach. The possible interpretation of the latter results is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better explain the relation between the current mass and the dynamical mass ansatz. Minor misprints corrected. Version to appear in Phys. Rev.

Screening of the topological charge in a correlated instanton vacuum

Screening of the topological charge due to he fermion-induced interactions is an important phenomenon, closely related with the resolution of the strong CP and U(1) problems. We study the mechanism of such screening in a 'correlated instanton vacuum', as opposed to the 'random' one. Both scalar and pseudoscalar gluonic correlators are analyzed by means of an observable that minimizes finite size effects. Screening of the topological charge is established. This allows us to calculate the $\eta'$ mass without having to invert the Dirac operator. We suggest that this method might be used in lattice QCD calculations as well. Our results for the screening of the topological charge are in agreement with the chiral Ward identities, and the scalar gluonic correlator satisfies a low energy theorem first derived by Novikov et al. \cite{Novikov-etal}. We also propose to evaluate the topological susceptibility in the Witten-Veneziano formula not in an infinite box in an world $without$ fermions but in an infinitesimal box in a world $with$ fermions.Comment: 22 pages + 5 postscript figures, SUNY-NTG/94-25. Corrected LATEX erro

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit