Renormalization of Matter Field Theories on the Lattice and the Flow Equation

We give a new proof of the renormalizability of a class of matter field theories on a space-time lattice; in particular we consider $\phi^4$ and massive Yukawa theories with Wilson fermions. We use the Polchinski approach to renormalization, which is based on the Wilson flow equation; this approach is substantially simpler than the BPHZ method, applied to the lattice by Reisz. We discuss matter theories with staggered fermions. In particular we analyse a simple kind of staggered fermions with minimal doubling, using which we prove the renormalizability of a chiral sigma model with exact chiral symmetry on the lattice.Comment: 32 pages, Late

Chiral symmetry restoration and axial vector renormalization for Wilson fermions

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.Comment: 11 pages, Latex2

Chiral gauge theories on the lattice with exact gauge invariance

A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.Comment: Talk given at the International Symposium on Lattice Field Theory (June 29--July 3, 1999, Pisa, Italy), 10 pages, latex source, style file include

Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such as Monte Carlo simulations. Our computational tools are illustrated at the example of scalar O(N) models with four and six-point couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and tarred tex file hdth9607.te

Lattice supersymmetry, superfields and renormalization

We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent anticommuting supersymmetries. We introduce a superfield formalism, which allows the enumeration of all possible lattice supersymmetry invariants. We use it to discuss the formulation of Q-exact lattice actions and their renormalization in a general manner. In some examples, one exact supersymmetry guarantees finiteness of the continuum limit of the lattice theory. As a consequence, we show that the desired quantum continuum limit is obtained without fine tuning for these models. Finally, we discuss the implications and possible further applications of our results to the study of gauge and non-gauge models.Comment: 44 pages, 1 figur

The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (``master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.Comment: 9 pages, 2 figure

Gauge invariant action at the ultraviolet cutoff

We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry.Comment: 5 pages, Latex, no figure

Three-Dimensional SU(3) gauge theory and the Spatial String Tension of the (3+1)-Dimensional Finite Temperature SU(3) Gauge Theory

We establish a close relation between the spatial string tension of the (3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($\sigma_s$) and the string tension of the 3-dimensional $SU(3)$ gauge theory ($\sigma_3$) which is similar to what has been found previously for $SU(2)$. We obtain $\sqrt{\sigma_3} = (0.554 \pm 0.004) g_3^2$ and $\sqrt{\sigma_s} = (0.586 \pm 0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical temperature results are consistent with a temperature dependent coupling running according to the two-loop $\beta$-function with $\Lambda_T = 0.118(36)T_c$.Comment: 11 pages (4 figures

Hadronic screening masses and the magnetic gluon condensate at high temperature

The hadronic screening mass at high temperature ($T$) in QCD$_4$ is examined on the basis of the QCD sum rules in (2+1) dimensions. Due to the magnetic gluon condensate at high $T$ which is expected to be nonvanishing, the screening mass deviates from the asymptotic value $2\pi T$. Also, the screening mass in the vector (pseudo-vector) channel turns out to be heavier than that in the scalar (pseudo-scalar) channel.Comment: 9 pages (LaTeX) +3 figures (available on request), KUNS 128

A Juvenile Specimen of the Trematopid Acheloma From Richards Spur, Oklahoma and Challenges of Trematopid Ontogeny

Trematopids are a clade of terrestrial dissorophoid temnospondyls documented primarily from terrestrial Permo-Carboniferous environments in North America and Europe. Here we describe the complete skull and articulated mandibles of a diminutive trematopid specimen (OMNH 79318) from the Early Permian karst deposits near Richards Spur, Oklahoma. Based on aspects of the neurocranium (e.g., unossified sphenethmoid, prootics, epipterygoids), the specimen represents one of the best examples of a markedly immature trematopid, an important data point for understanding the early ontogeny of trematopids. Specifically, it provides evidence that variation in otic notch structure can be ontogenetically influenced, not only among eucacopine dissorophids but also among trematopids. We provisionally refer the specimen to cf. Acheloma based on the presence of a denticulate vomerine ridge and other qualitative features. However, we emphasize that the taxonomic referral is complicated by several factors that more broadly confound trematopid taxonomy. This includes a low sample size (n = 1) of many taxa and marked size, and presumed ontogenetic, disparity between the known size range of different taxa. Complementary reexamination of both Acheloma cumminsi and Acheloma dunni as part of this study also reveals that the former possesses lateral exposures of palatal bones, the presence/absence of which was the only formal character that previously differentiated the two species, although other qualitative features (e.g., size of the internarial fontanelle) may differentiate these two species. With respect to OMNH 79318, the taxonomic referral is tentative because the specimen also shares many qualitative attributes with Phonerpeton pricei, a trematopid represented only by small-bodied, probably immature individuals. However, many of these shared features are likely to be influenced by ontogeny or size. The subsequent challenges that we encountered in our taxonomic referral suggest that ontogeny may be confounding taxonomy in both diagnoses and phylogenetic analyses of trematopids and emphasize the need for careful study of how this affects our understanding of trematopid intrarelationships