Phase structure of NJL model with finite quark mass and QED correction

We study QED corrections to the chiral symmetry breaking in Nambu-Jona-Lasinio (NJL) model with two flavors of quarks. In the model the isospin symmetry is broken by differences of the current quark masses and the electromagnetic charges between up and down quarks. In the leading order of the 1/N expansion we calculate the effective potential of the model with one-loop QED corrections. Evaluating the effective potential, we study an influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass has an important contribution for the orientation of chiral symmetry breaking.Comment: 7 pages, 8 figures, To appear in the proceedings of the Workshop on Origin of Mass and Strong Coupling Gauge Theories, Nagoya, Japan, 21-24 November 200

Constraint on ghost-free bigravity from gravitational Cherenkov radiation

We investigate gravitational Cherenkov radiation in a healthy branch of background solutions in the ghost-free bigravity model. In this model, because of the modification of dispersion relations, each polarization mode can possess subluminal phase velocities, and the gravitational Cherenkov radiation could be potentially emitted from a relativistic particle. In the present paper, we derive conditions for the process of the gravitational Cherenkov radiation to occur and estimate the energy emission rate for each polarization mode. We found that the gravitational Cherenkov radiation emitted even from an ultrahigh energy cosmic ray is sufficiently suppressed for the graviton's effective mass less than $100\,{\rm eV}$, and the bigravity model with dark matter coupled to the hidden metric is therefore consistent with observations of high energy cosmic rays.Comment: 13 pages, 2 figures; v

On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories

We study $SU(2)$ gauge theories coupled to $(A_1,D_N)$ theories with or without a fundamental hypermultiplet. For even $N$, a formula for the contribution of $(A_1,D_N)$ to the Nekrasov partition function was recently obtained by us with Y.~Sugawara and T.~Uetoko. In this paper, we generalize it to the case of odd $N$ in the classical limit, under the condition that the relevant couplings and vacuum expectation values of Coulomb branch operators of $(A_1,D_N)$ are all turned off. We apply our formula to the $(A_2,A_5)$ theory to find that its prepotential is related to that of the $SU(2)$ gauge theory with four fundamental flavors by a simple change of variables.Comment: 34 pages, 4 figure

On variations of Yama Nim and Triangular Nim

Yama Nim is a two heaps Nim game introduced in the second author's Master Thesis, where the player takes more than $2$ tokens from one heap, and return $1$ token to the other heap. Triangular Nim is a generalization, where the player takes several tokens from one heap, and return some tokens (at least one token) to the other heap, so that the total number of the tokens in the heaps decrease strictly. In this paper, we investigate their winning strategies, Grundy numbers, and their variations and generalizations. Particularly interesting is the Wythoff variations, where in addition to the Yama/Triangular Nim moves, the player is allowed to take tokens from both heaps, say $i$ tokens from the first heap and $j$ tokens from the other, under some restrictions for $i$ and $j$. For example when we force $i=j>0$ for the Triangular Nim, then the pair of non-negative integers $(x, y)$ with $x$ less than or equal to $y$ is in the $P$-position if and only if $(x, y) is in {(0, 0), (0, 1), (1, 3), (3, 6), (6, 10), (10, 15), ...}$, namely the winning strategy is described by triangular numbers. In other rulesets, we also found examples where the square numbers, pentagonal numbers, geometric progressions, and so on.Comment: 20 page

DRAM-cell-based multiple-valued logic-in-memory VLSI with charge addition and charge storage

科研費報告書収録論文(課題番号:12480064・基盤研究(B)(2) ・H12～H14/研究代表者:亀山, 充隆/配線ボトルネックフリー2線式多値ディジタルコンピューティングVLSIシステム

Multiple-valued content-addressable memory using metal-ferroelectric-semiconductor FETs

科研費報告書収録論文(課題番号:09558027・基盤研究(B)(2)・H9～H12/研究代表者:羽生, 貴弘/1トランジスタセル多値連想メモリの試作とその応用