Brane Creation in M(atrix) Theory

We discuss, in the context of M(atrix) theory, the creation of a membrane suspendend between two longitudinal five-branes when they cross each other. It is shown that the membrane creation is closely related to the degrees of freedom in the off-diagonal blocks which are related via dualities to the chiral fermionic zero mode on a 0-8 string. In the dual system of a D0-brane and a D8-brane in type \IIA theory the half-integral charges associated with the ``half''-strings are found to be connected to the well-known fermion-number fractionalization in the presence of a fermionic zero mode. At sufficiently short distances, the effective potential between the two five-branes is dominated by the zero mode contribution to the vacuum energy.Comment: 14 pages, Latex. A new paragraph on p.10 and acknowledgement added. v3: The version for publication: minor revisions and typos correcte

P-p′ strings in M(atrix) theory

ManuscriptWe study the off-diagonal blocks in the M(atrix) model that are supposed to correspond to open strings stretched between a Dp-brane and a Dp′-brane. It is shown that the spectrum, including the quantum numbers, of the zero modes in the off-diagonal blocks can be determined from the index theorem and unbroken supersymmetry, and indeed reproduces string theory predictions for p-p′ strings. Previously the matrix description of a longitudinal fivebrane needed to introduce extra degrees of freedom corresponding to 0-4 strings by hand. We show that they are naturally associated with the off-diagonal zero modes, and the supersymmetry transformation laws and low energy effective action postulated for them are now derivable from the M(atrix) theory

Mutual exclusion statistics between quasiparticles in the fractional quantum Hall effect

Journal ArticleIn this paper we propose a new assignment for mutual exclusion statistics between quasielectrons and quasiholes in the fractional quantum Hall effect. In addition to providing numerical evidence for this assignment, we show that the physical origin of this mutual statistics is a novel hard-core constraint due to correlation between the distinguishable vortexlike quasiparticles

Type-IIB-string-M-theory duality and longitudinal membranes in M(atrix) theory

Journal ArticleIn this paper we study duality properties of the M(atrix) theory compactified on a circle. We present evidence for the equivalence of this theory to the strong coupling limit of type-IIB string theory compactified on a circle. In the M(atrix) theory context, our evidence for this duality consists of showing the appearance (upon compactification) of a topological term recently discovered in the D-string action, identifying the BPS states of type-IIB strings in the spectrum and finding the remnant symmetry of SL(2,Z) and the associated t moduli. By this type-IIB-string-M-theory duality, a number of insights are gained into the physics of longitudinal membranes in the infinite momentum frame

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach with Linear Convergence

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly desirable to design decentralized algorithms that can handle stochastic communication networks. However, most existing algorithms for DCCO only work in time-invariant networks and cannot be extended to stochastic networks because they inherently need knowledge of network topology $\textit{a priori}$. In this paper, we propose a new decentralized dual averaging (DDA) algorithm that can solve DCCO in stochastic networks. Under a rather mild condition on stochastic networks, we show that the proposed algorithm attains $\textit{global linear convergence}$ if each local objective function is strongly convex. Our algorithm substantially improves the existing DDA-type algorithms as the latter were only known to converge $\textit{sublinearly}$ prior to our work. The key to achieving the improved rate is the design of a novel dynamic averaging consensus protocol for DDA, which intuitively leads to more accurate local estimates of the global dual variable. To the best of our knowledge, this is the first linearly convergent DDA-type decentralized algorithm and also the first algorithm that attains global linear convergence for solving DCCO in stochastic networks. Numerical results are also presented to support our design and analysis.Comment: 22 pages, 2 figure