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

A Perturbative Construction of Lattice Chiral Fermions

We perform a renormalization group transformation to construct a lattice theory of chiral fermions. The field variables of the continuum theory are averaged over hypercubes to define lattice fields. Integrating out the continuum variables in perturbation theory we derive a chirally invariant effective action for the lattice fields. This is consistent with the Nielsen-Niniomiya theorem because the effective action is nonlocal. We also construct the axial current on the lattice and we show that the axial anomaly of the continuum theory is reproduced in the Schwinger model. This shows that chiral fermions can be regularized on the lattice.Comment: 8 pages, LaTe

Disorganized attachment and defense: exploring John Bowlby's unpublished reflections.

Main and Solomon were the first to create a formal infant Strange Situation classification of attachment disorganization. Bowlby's reflections on the underlying psychological processes of such behaviors, however, began early in his career, including the term "disorganization." Most of these remained unpublished but are available through the John Bowlby Archive. Bowlby saw affective experiences as the source of the attachment behavioral system's organization and regulation, and he introduced the term "effector equipment" to describe the emergent organization of attention, expectation, affect, and behavior to orchestrate responses to the environment. In his thinking, disorganization results from threat conflict, safe haven ambiguity, and/or activation without assuagement, which interfere with coordination and integration across a behavioral system. Bowlby's unpublished writings also amplify his published work on segregated systems and defensive exclusion. Bowlby's insights are relevant today and can provide greater background and clarity to current work, as researchers and clinicians consider the origins, manifestations, and meaning of disorganization

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

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

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

Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point

We compute the non--trivial infrared $\phi^4_3$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate representation for the fixed point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponent $\nu$ up to order twenty five of interpolation expansion in this representation, and evaluate it using \pade, Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The resummation returns $0.6262(13)$ as the value of $\nu$.Comment: 29 pages, Latex2e, 2 Postscript figure

A New Captorhinid From the Permian Cave System Near Richards Spur, Oklahoma, and the Taxic Diversity of Captorhinus at This Locality

The early Permian cave system in the Dolese Brothers Limestone Quarry near Richards Spur, Oklahoma represents a unique depositional environment that has been interpreted as preserving an upland biota. The quarry and the region around it represent Paleozoic cave systems that underwent periods of flooding not unlike present-day conditions that are commonly associated with monsoonal episodes. The Richards Spur locality is particularly rich in captorhinid eureptiles which represent one of the earliest reptilian clades to have evolved a specialized dentition. Although the multiple-tooth rowed Captorhinus aguti is the most abundant captorhinid at Richards Spur, at least one other species has been described (Captorhinus magnus) and assigned to the same genus, but five other captorhinid taxa have also been found. We describe a new member of the genus Captorhinus (Captorhinus kierani) and explore details of the dental anatomy against the two other members of the genus at Richards Spur, C. aguti and C. magnus, as well as with a member of the genus not presently known from Richards Spur (Captorhinus laticeps). Findings suggest that the nature of the ogival dentition described previously as a synapomorphy uniting C. aguti with C. magnus is not supported and we propose a more informative method for differentiating among dental characters within the clade. The discovery of a new species of Captorhinus provides additional evidence for captorhinid taxic diversity at Richards Spur and is supportive of niche partitioning, which is likely associated with reducing intra-specific competition within the clade. In addition, we argue that the captorhinid fossils at Richards Spur likely includes one additional, currently undescribed multiple-tooth rowed form, that renders the current practice of assigning disarticulated cranial remains, specifically dental fragments, to the species C. aguti problematic. Finally, we offer a method for a comprehensive examination of the dental characteristics, which can then be applied to explore taxic diversity at Richards Spur and examine one of the earliest examples of niche specialization. As a consequence of this research, additional insight into exploring biological interactions between Paleozoic taxa can be examined, with an opportunity to shed light on what might have driven these evolutionary processes

Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model

The recently developed Meron-Cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a four-fermion interaction. This model cannot be explored using standard algorithms. We find that the Z(2) chiral symmetry of this model is spontaneously broken at low temperatures and that the finite-temperature chiral phase transition is in the universality class of the 2-d Ising model, as expected.Comment: 18 pages, LaTe

Precise determination of critical exponents and equation of state by field theory methods

Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized phi^4_3 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N-vector model (R. Guida and J. Zinn-Justin, J. Phys. A31 (1998) 8103. cond-mat/9803240). and of the equation of state of the 3D Ising model (R. Guida and J. Zinn-Justin, Nucl. Phys. B489 [FS] (1997) 626, hep-th/9610223.). These results are among the most precise available probing field theory in a non-perturbative regime.Comment: 23 pages, tex, private macros, one figur