Supersymmetric theories on squashed five-sphere

We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.Comment: 20 pages, no figure, LaTeX; v3: minor corrections, accepted for publication in PTE

A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality

We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE \p_t u=-X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu), associated to a system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in \Om\times (0,T) with \Om \subset M an open subset of a manifold $M$ with control metric $d$ corresponding to $X$ and a measure $d\sigma$ follows from the basic hypothesis of doubling condition and a weak Poincar\'e inequality. We also show that such hypothesis hold for a class of Riemannian metrics g_\e collapsing to a sub-Riemannian metric \lim_{\e\to 0} g_\e=g_0 uniformly in the parameter \e\ge 0

Comment on "Single-mode excited entangled coherent states"

In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors claim that, for single-mode excited entangled coherent states $| \Psi_{\pm}(\alpha,m)>$, \textquotedblleft the photon excitations lead to the decrease of the concurrence in the strong field regime of $| \alpha | ^{2}$ and the concurrence tends to zero when $| \alpha | ^{2}\to \infty$". This is wrong.Comment: 4 apges, 2 figures, submitted to JPA 15 April 200

SU(6)⊃\supsetSU(3)xSU(2) and SU(8)⊃\supsetSU(4)xSU(2) Clebsch-Gordan coefficients

Tables of scalar factors are presented for 63x63 and 120x63 in SU(8)$\supset$SU(4)xSU(2), and for 35x35 and 56x35 in SU(6)$\supset$SU(3)xSU(2). Related tables for SU(4)$\supset$SU(3)xU(1) and SU(3)$\supset$SU(2)xU(1) are also provided so that the Clebsch-Gordan coefficients can be completely reconstructed. These are suitable to study meson-meson and baryon-meson within a spin-flavor symmetric scheme.Comment: 30 pages, mostly table

More Dynamical Supersymmetry Breaking

In this paper we introduce a new class of theories which dynamically break supersymmetry based on the gauge group SU(n)xSU(3)xU(1) for even n. These theories are interesting in that no dynamical superpotential is generated in the absence of perturbations. For the example SU(4)xSU(3)xU(1) we explicitly demonstrate that all flat directions can be lifted through a renormalizable superpotential and that supersymmetry is dynamically broken. We derive the exact superpotential for this theory, which exhibits new and interesting dynamical phenomena. For example, modifications to classical constraints can be field dependent. We also consider the generalization to SU(n)xSU(3)xU(1) models (with even n>4). We present a renormalizable superpotential which lifts all flat directions. Because SU(3) is not confining in the absence of perturbations, the analysis of supersymmetry breaking is very different in these theories from the n=4 example. When the SU(n) gauge group confines, the Yukawa couplings drive the SU(3) theory into a regime with a dynamically generated superpotential. By considering a simplified version of these theories we argue that supersymmetry is probably broken.Comment: 21 pages, LaTe

Structural and optical properties of MOCVD AllnN epilayers

7] M.-Y. Ryu, C.Q. Chen, E. Kuokstis, J.W. Yang, G. Simin, M. Asif Khan, Appl. Phys. Lett. 80 (2002) 3730. [8] D. Xu, Y. Wang, H. Yang, L. Zheng, J. Li, L. Duan, R. Wu, Sci. China (a) 42 (1999) 517. [9] H. Hirayama, A. Kinoshita, A. Hirata, Y. Aoyagi, Phys. Stat. Sol. (a) 188 (2001) 83. [10] Y. Chen, T. Takeuchi, H. Amano, I. Akasaki, N. Yamada, Y. Kaneko, S.Y. Wang, Appl. Phys. Lett. 72 (1998) 710. [11] Ig-Hyeon Kim, Hyeong-Soo Park, Yong-Jo Park, Taeil Kim, Appl. Phys. Lett. 73 (1998) 1634. [12] K. Watanabe, J.R. Yang, S.Y. Huang, K. Inoke, J.T. Hsu, R.C. Tu, T. Yamazaki, N. Nakanishi, M. Shiojiri, Appl. Phys. Lett. 82 (2003) 718