Four-dimensional lattice chiral gauge theories with anomalous fermion content

In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.Comment: 18 pages, the final version to appear in JHE

Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions

Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.Comment: LaTeX, 10 page

More about the axial anomaly on the lattice

We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-abelian gauge groups, we propose a conjecture on a possible form of axial anomaly on the infinite lattice, which holds to all orders in perturbation theory. With this conjecture, we show that a structure of the axial anomaly on finite-size lattices is again basically identical to that on the infinite lattice. Our analysis with the Ginsparg-Wilson Dirac operator indicates that, in appropriate frameworks, the basic structure of axial anomaly is quite robust and it persists even in a system with finite ultraviolet and infrared cutoffs.Comment: 12 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in Nucl. Phys.

Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator

The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.Comment: 11 pages, uses PHYZZX, evaluation of lattice integrals is revised. The final version to appear in Prog. Theor. Phy

Chiral anomalies in the reduced model

On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$ limit when d>2.Comment: 20 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE

Arachidonic acid production by the oleaginous fungus Mortierella alpina 1S-4 : A review

The filamentous fungus Mortierella alpina 1S-4 is capable of accumulating a large amount of triacylglycerol containing C20 polyunsaturated fatty acids (PUFAs). Indeed, triacylglycerol production by M. alpina 1S-4 can reach 20 g/L of culture broth, and the critical cellular signaling and structural PUFA arachidonic acid (ARA) comprises 30%–70% of the total fatty acid. The demonstrated health benefits of functional PUFAs have in turn encouraged the search for rich sources of these compounds, including fungal strains showing enhanced production of specific PUFAs. Screening for mutants and targeted gene manipulation of M. alpina 1S-4 have elucidated the functions of various enzymes involved in PUFA biosynthesis and established lines with improved PUFA productivity. In some cases, these strains have been used for indistrial-scale production of PUFAs, including ARA. In this review, we described practical ARA production through mutant breeding, functional analyses of genes encoding enzymes involved in PUFA biosynthesis, and recent advances in the production of specific PUFAs through molecular breeding of M. alpina 1S-4

Topological Obstruction in Block-spin Transformations

Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operators. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables.Comment: 11 pages, latex, no figure