Comments on Large N Matrix Model

The large N Matrix model is studied with attention to the quantum fluctuations around a given diagonal background. Feynman rules are explicitly derived and their relation to those in usual Yang-Mills theory is discussed. Background D-instanton configuration is naturally identified as a discretization of momentum space of a corresponding QFT. The structure of large N divergence is also studied on the analogy of UV divergences in QFT.Comment: 32 pages, 9 figure

D-brane actions on Kähler manifolds

We consider actions for N D-branes at points in a general Kähler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining M(atrix)-theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in M(atrix)-theory

Modular invariance of string theory on AdS_3

We discuss the modular invariance of the SL(2,R) WZW model. In particular, we discuss in detail the modular invariants using the \hat{sl}(2,R) characters based on the discrete unitary series of the SL(2,R) representations. The explicit forms of the corresponding characters are known when no singular vectors appear. We show, for example, that from such characters modular invariants can be obtained only when the level k < 2 and infinitely large spins are included. In fact, we give a modular invariant with three variables Z(z,\tau, u) in this case. We also argue that the discrete series characters are not sufficient to construct a modular invariant compatible with the unitarity bound, which was proposed to resolve the ghost problem of the SL(2,R) strings.Comment: 12 pages, no figures, latex; v2: a reference added, minor corrections; v3: some changes in presentation, version to appear in Phys. Lett.

D-brane actions on Kähler manifolds

We consider actions for N D-branes at points in a general Kähler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining M(atrix)-theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in M(atrix)-theory

Free Boson Representation of qq-Vertex Operators and their Correlation Functions

A bosonization scheme of the $q$-vertex operators of \uqa for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed for $N$-point functions and explicit calculation for two-point function is presented.Comment: 22 pages, latex file, UT-618 (revised version

Zonotopes and four-dimensional superconformal field theories

The a-maximization technique proposed by Intriligator and Wecht allows us to determine the exact R-charges and scaling dimensions of the chiral operators of four-dimensional superconformal field theories. The problem of existence and uniqueness of the solution, however, has not been addressed in general setting. In this paper, it is shown that the a-function has always a unique critical point which is also a global maximum for a large class of quiver gauge theories specified by toric diagrams. Our proof is based on the observation that the a-function is given by the volume of a three dimensional polytope called "zonotope", and the uniqueness essentially follows from Brunn-Minkowski inequality for the volume of convex bodies. We also show a universal upper bound for the exact R-charges, and the monotonicity of a-function in the sense that a-function decreases whenever the toric diagram shrinks. The relationship between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version published in JHE

Two genetic variants of CD38 in subjects with autism spectrum disorder and controls

金沢大学医薬保健研究域医学系The neurobiological basis of autism spectrum disorder (ASD) remains poorly understood. Given the role of CD38 in social recognition through oxytocin (OT) release, we hypothesized that CD38 may play a role in the etiology of ASD. Here, we first examined the immunohistochemical expression of CD38 in the hypothalamus of post-mortem brains of non-ASD subjects and found that CD38 was colocalized with OT in secretory neurons. In studies of the association between CD38 and autism, we analyzed 10 single nucleotide polymorphisms (SNPs) and mutations of CD38 by re-sequencing DNAs mainly from a case-control study in Japan, and Caucasian cases mainly recruited to the Autism Genetic Resource Exchange (AGRE). The SNPs of CD38, rs6449197 (p 70; designated as high-functioning autism (HFA)) in the U.S. 104 AGRE family trios, but not with Japanese 188 HFA subjects. A mutation that caused tryptophan to replace arginine at amino acid residue 140 (R140W; (rs1800561, 4693C>T)) was found in 0.6-4.6% of the Japanese population and was associated with ASD in the smaller case-control study. The SNP was clustered in pedigrees in which the fathers and brothers of T-allele-carrier probands had ASD or ASD traits. In this cohort OT plasma levels were lower in subjects with the T allele than in those without. One proband with the T allele who was taking nasal OT spray showed relief of symptoms. The two variant CD38 poloymorphysms tested may be of interest with regard of the pathophysiology of ASD. © 2010 Elsevier Ireland Ltd and the Japan Neuroscience Society