Meta-Stable Brane Configurations by Higher Order Polynomial Superpotential

We construct the type IIA nonsupersymmetric meta-stable brane configuration consisting of (2k+1) NS5-branes and D4-branes where the electric gauge theory superpotential has an order (2k+2) polynomial for the bifundamentals. We find a rich pattern of nonsupersymmetric meta-stable states as well as the supersymmetric stable ones. By adding the orientifold 4-plane to this brane configuration, we also describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of corresponding gauge theory.Comment: 27pp, 8 figures; some footnotes added; to appear in IJMP

Explicit Construction of Spin 4 Casimir Operator in the Coset Model SO^(5)1×SO^(5)m/SO^(5)1+m \hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m}

We generalize the Goddard-Kent-Olive (GKO) coset construction to the dimension 5/2 operator for $\hat{so} (5)$ and compute the fourth order Casimir invariant in the coset model $\hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m}$ with the generic unitary minimal $c < 5/2$ series that can be viewed as perturbations of the $m \rightarrow \infty$ limit, which has been investigated previously in the realization of $c= 5/2$ free fermion model.Comment: 11 page

Combinatorial Voting

We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner. © 2012 The Econometric Society

Multi-population genetic algorithms with immigrants scheme for dynamic shortest path routing problems in mobile ad hoc networks

Copyright @ Springer-Verlag Berlin Heidelberg 2010.The static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless mesh network, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP problem turns out to be a dynamic optimization problem in mobile wireless networks. In this paper, we propose to use multi-population GAs with immigrants scheme to solve the dynamic SP problem in MANETs which is the representative of new generation wireless networks. The experimental results show that the proposed GAs can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.This work was supported by the Engineering and Physical Sciences Research Council(EPSRC) of UK under Grant EP/E060722/1

Perturbing Around A Warped Product Of AdS_4 and Seven-Ellipsoid

We compute the spin-2 Kaluza-Klein modes around a warped product of AdS_4 and a seven-ellipsoid. This background with global G_2 symmetry is related to a U(N) x U(N) N=1 superconformal Chern-Simons matter theory with sixth order superpotential. The mass-squared in AdS_4 is quadratic in G_2 quantum number and KK excitation number. We determine the dimensions of spin-2 operators using the AdS/CFT correspondence. The connection to N=2 theory preserving SU(3) x U(1)_R is also discussed.Comment: 21pp; The second and last paragraphs of section 2, the footnotes 1 and 2 added and to appear in JHE

The Full Structure of Quantum N=2N=2 Super-W3(2)W_3^{(2)} Algebra

We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with integer spins 1 and 2, besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras. For $c\rightarrow \infty$ limit, the algebra reduces to the classical one, which has been studied previously. The 'hybrid' field realization of this algebra is also discussed.Comment: 8 pages, latex, no figure

Geometrically Induced Phase Transitions at Large N

Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure

Meta-Stable Brane Configurations by Adding an Orientifold-Plane to Giveon-Kutasov

In hep-th/0703135, they have found the type IIA intersecting brane configuration where there exist three NS5-branes, D4-branes and anti-D4-branes. By analyzing the gravitational interaction for the D4-branes in the background of the NS5-branes, the phase structures in different regions of the parameter space were studied in the context of classical string theory. In this paper, by adding the orientifold 4-plane and 6-plane to the above brane configuration, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of these gauge theories.Comment: 21 pp, 6 figures; reduced bytes of figures, DBI action analysis added and to appear in JHE