New Discrete States in Two-Dimensional Supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.Comment: 22 pages; typos corrected, 2 references adde

Gravitational Couplings of Higher Spins from String Theory

We calculate the interaction 3-vertex of two massless spin 3 particles with a graviton using vertex operators for spin 3 fields in open string theory, constructed in our previous work. The massless spin 3 fields are shown to interact with the graviton through the linearized Weyl tensor, reproducing the result by Boulanger, Leclercq and Sundell. This is consistent with the general structure of the non-Abelian $2-s-s$ couplings, implying that the minimal number of space-time derivatives in the interaction vertices of two spin s and one spin 2 particle is equal to $2s-2$.Comment: 19 page

A Message Passing Strategy for Decentralized Connectivity Maintenance in Agent Removal

In a multi-agent system, agents coordinate to achieve global tasks through local communications. Coordination usually requires sufficient information flow, which is usually depicted by the connectivity of the communication network. In a networked system, removal of some agents may cause a disconnection. In order to maintain connectivity in agent removal, one can design a robust network topology that tolerates a finite number of agent losses, and/or develop a control strategy that recovers connectivity. This paper proposes a decentralized control scheme based on a sequence of replacements, each of which occurs between an agent and one of its immediate neighbors. The replacements always end with an agent, whose relocation does not cause a disconnection. We show that such an agent can be reached by a local rule utilizing only some local information available in agents' immediate neighborhoods. As such, the proposed message passing strategy guarantees the connectivity maintenance in arbitrary agent removal. Furthermore, we significantly improve the optimality of the proposed scheme by incorporating $\delta$-criticality (i.e. the criticality of an agent in its $\delta$-neighborhood).Comment: 9 pages, 9 figure