Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

Effective Average Action in N=1 Super-Yang-Mills Theory

For N=1 Super-Yang-Mills theory we generalize the effective average action Gamma_k in a manifest supersymmetric way using the superspace formalism. The exact evolution equation for Gamma_k is derived and, introducing as an application a simple truncation, the standard one-loop beta-function of N=1 SYM theory is obtained.Comment: 17 pages, LaTeX, some remarks added, misprints corrected, to appear in Phys. Rev.

The beta functions of a scalar theory coupled to gravity

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.Comment: 13 pages, plainTe

Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice

We continue to construct lattice super Yang-Mills theories along the line discussed in the previous papers \cite{sugino, sugino2}. In our construction of ${\cal N}=2, 4$ theories in four dimensions, the problem of degenerate vacua seen in \cite{sugino} is resolved by extending some fields and soaking up would-be zero-modes in the continuum limit, while in the weak coupling expansion some surplus modes appear both in bosonic and fermionic sectors reflecting the exact supersymmetry. A slight modification to the models is made such that all the surplus modes are eliminated in two- and three-dimensional models obtained by dimensional reduction thereof. ${\cal N}=4, 8$ models in three dimensions need fine-tuning of three and one parameters respectively to obtain the desired continuum theories, while two-dimensional models with ${\cal N}=4, 8$ do not require any fine-tuning.Comment: 28 pages, no figure, LaTeX, JHEP style; (v2) published version to JHEP; (v3) argument on the vacuum degeneracy revised, 34 page

Deconstruction and other approaches to supersymmetric lattice field theories

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.Comment: 70 page

Wess-Zumino model with exact supersymmetry on the lattice

A lattice formulation of the four dimensional Wess-Zumino model that uses Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The supersymmetry transformation that leaves invariant the action at finite lattice spacing is determined by performing an iterative procedure in the coupling constant. The closure of the algebra, generated by this transformation is also showed.Comment: 13 pages. Few references added. New appendix on Ward identity added. Version to be published in JHE

Lattice formulation of N=4{\cal N}=4 super Yang-Mills theory

We construct a lattice action for ${\cal N}=4$ super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation that the fermions of the continuum theory can be mapped into the component fields of a single real anticommuting Kahler-Dirac field. The original supersymmetry algebra then implies the existence of a nilpotent scalar supercharge $Q$ and a corresponding set of bosonic superpartners. Using this field content we write down a $Q$-exact action and show that, with an appropriate change of variables, it reduces to a well-known twist of ${\cal N}=4$ super Yang-Mills theory due to Marcus. Using the discretization prescription developed in an earlier paper on the ${\cal N}=2$ theory in two dimensions we are able to translate this geometrical action to the lattice.Comment: 15 pages. 1 reference correcte

Effective Action for the Quark-Meson Model

The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between quarks and mesons the low momentum physics is essentially determined by infrared fixed points. This allows us to establish relations between various parameters related to the meson potential. The results for $f_\pi$ and \VEV{\olpsi\psi} are not very sensitive to the poorly known details of the quark--meson effective action at scales where the mesonic bound states form. For realistic constituent quark masses we find $f_\pi$ around 100\MeV.Comment: 56 pages (including 10 figures and 1 table), uses epsf.st

Gluon Condensation in Nonperturbative Flow Equations

We employ nonperturbative flow equations for an investigation of the effective action in Yang-Mills theories. We compute the effective action $\Gamma[B]$ for constant color magnetic fields $B$ and examine Savvidy's conjecture of an unstable perturbative vacuum. Our results indicate that the absolute minimum of $\Gamma[B]$ occurs for B=0. Gluon condensation is described by a nonvanishing expectation value of the regularized composite operator $F_{\mu\nu}F^{\mu\nu}$ which agrees with phenomenological estimates.Comment: 64 pages, late

Space-Time Supersymmetry of Extended Fermionic Strings in 2+22 + 2 Dimensions

The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings living in uncompactified $2 + 2$ dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of $SO(2,2)$ Lorentz symmetry as well as at least one self-dual space-time supersymmetry in the theory of the $N=2(4)$ fermionic strings, though we do not have a compelling reason to argue about the necessity of the {\it maximal} space-time supersymmetry. The world-sheet arguments about the absence of all string massive modes in the physical spectrum, and the vanishing of all string-loop amplitudes in the Polyakov approach, are given on the basis of general consistency of the theory.Comment: 29 pages, LaTeX, ITP-UH-1/9