An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry -Summary of the Formulation-

We propose a lattice field theory formulation which overcomes some fundamental difficulties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the lattice, the star product, and the chiral fermion species doublers degrees of freedom can be avoided consistently. This framework is general enough to formulate non-supersymmetric lattice field theory without chiral fermion problem. This lattice formulation has a nonlocal nature and is essentially equivalent to the corresponding continuum theory. We can show that the locality of the star product is recovered exponentially in the continuum limit. Possible regularization procedures are proposed.The associativity of the product and the lattice translational invariance of the formulation will be discussed.Comment: 14 pages, Lattice2017 Proceeding

An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry

We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree of freedom on the lattice corresponds to $2^d$ degrees of freedom in the continuum, but all these doublers have (in the case of fermions) the same chirality and can be either identified, thus removing the degeneracy, or, in some theories with extended supersymmetry, identified with different members of the same supermultiplet. 2) The derivative operator, defined on the lattice as a suitable periodic function of the lattice momentum, is an addittive and conserved quantity, thus assuring that the Leibnitz rule is satisfied. This implies that the product of two fields on the lattice is replaced by a non-local "star product" which is however in general non-associative. Associativity of the "star product" poses strong restrictions on the form of the lattice derivative operator (which becomes the inverse gudermannian function of the lattice momentum) and has the consequence that the degrees of freedom of the lattice theory and of the continuum theory are in one-to-one correspondence, so that the two theories are eventually equivalent. Regularization of the ultraviolet divergences on the lattice is not associated to the lattice spacing, which does not act as a regulator, but may be obtained by a one parameter deformation of the lattice derivative, thus preserving the lattice structure even in the limit of infinite momentum cutoff. However this regularization breaks gauge invariance and a gauge invariant regularization within the lattice formulation is still lacking.Comment: 68 pages, 7 figure

Effect of fasting and re-feeding on aquaporin gene expression in liver and kidney of the chicken

　Aquaporin (AQP) which is a water channel, is also including the group (aquaglyceroporin) letting glycerol or urea go through as well as a water molecule. In mammals, AQP7 and AQP9 which are aquaglyceroporin have a role in the transportation of glycerol related to the gluconeogenesis in the liver. It is reported that AQP9 increases uptake of glycerol in the liver, when blood glucose level decreases. This study investigated the effect of AQP9 and AQP7 mRNA levels in liver and kidney in relation to the fasting and the re-feeding in the chicks. The purpose of this study was to determine whether the functions of AQP9 and AQP7 in the chicks are similar to mammals. One-day old chicks were kept with free access to water and food until 7-days old. At 7-days old, chicks were divided into three groups of 6 chicks : a control groups with free access to food and water and a fasting group with free access to water but not to water for 24 hours, a re-feeding group with free access to food and water for 6 hours after fasting treatment. At the end of the experiments all the chicks were sacrificed and blood and tissues (liver and kidney) were taken for measurement of blood glucose levels and mRNA levels. Total RNA extracted and reverse transcription was performed. AQP7 and AQP9 and the phosphoenolpyruvate carboxykinase (PEPCK) mRNA levels were measured by using real-time PCR. In the fasting group, body weight significantly decreased as compared with control group, but blood glucose levels did not decrease. In the re-feeding groups, blood glucose levels significantly increased as compared with control group and fasting group. In the liver, the fasting and the re-feeding treatment did not affect AQP7 and AQP9 mRNA levels. In the kidney, the fasting did not affect AQP7 and AQP9 mRNA levels, but the re-feeding treatment significantly increased AQP7 and AQP9 mRNA levels. In the liver, PEKCK mRNA levels significantly decreased in fasting group and further decreased in the re-feeding group. The re-feeding treatment significantly increased PEPCK mRNA levels in the kidney. From these results, kidney may play a roll in the increase of blood glucose levels at the re-feeding. But, a roll in gluconeogenesis of liver is not clear in the chicks. Therefore, further study is necessary to understand the gluconeogenesis in the chicks

Abnormality of water homeostasis of Muscular dystrophic chicken

The muscular dystrophy chicken has been studying as model animal of muscular dystrophy for more than 50 years. Recently, the mutation of WW domain containing E3 ubiquitin protein ligase 1 (WWP1) gene has been identified as a responsible for muscular dystrophy chicken. We observed that muscular dystrophy chicken not only showed the degeneration of skeletal muscles but also produced watery feces. Therefore, we examined the possibility of abnormalities in water metabolism of muscular dystrophy chicken. We first analyzed plasma osmolality and gene expression of aquaporin 2 (AQP2), AQP3 and alpha subunit of the amiloride-sensitive epithelial sodium channel (αENaC) in muscular dystrophy chicken and White Leghorn chicken under normal physiological conditions at five-week old. Subsequently, we analyzed these same parameters after one-day water-deprivation. The main findings of our study are that: I) the plasma osmolality was significantly higher in muscular dystrophic chicken than in White Leghorn; II) kidney αENaC mRNA expression was significantly lower in muscular dystrophic chicken than in White Leghorn; III) AQP2 and AQP3 mRNA expressions in muscular dystrophic chicken were similar in White Leghorn. We suggest that the mutation of WWP1 may cause the abnormality of sodium absorption, and thus muscular dystrophic chicken become hypernatremic

Sexual Dimorphism of Arginine Vasotocin Neuron in Birds

Arginine vasotocin (AVT) is one of neurohypophysial peptides in birds and is well known both as an antidiuretic and oxytocic hormone. AVT is produced in the hypothalamus and mainly synthesized in magnocellular neurons, supraoptic nucleus (SON) and paraventricular nucleus (PVN). Recent, immunocytochemistry and in situ hybridization results indicate that AVT is also synthesized in parvocellular neurons corresponding to mammalian stria terminalis (nST). The AVT neurons in nST in the male are more numerous than those in the female. Therefore, these data suggest that there is sexual dimorphism in the distribution of AVT neurons. Several experiments involving electrical lesion, testosterone implantation, and the detection of the immediately-early gene expression in birds expressing copulatory behavior suggested that nST and nucleus praeopticus medialis (POM) were related to the reproductive behavior. When male embryo was treated with estradiol, the distribution of AVT neurons assumes the same distribution as found in the female, and reproductive behavior was abolished, suggesting that AVT in the brain has an important role in reproductive behavior