Integrability in SFT and new representation of KP tau-function

We are investigating the properties of vacuum and boundary states in the CFT of free bosons under the conformal transformation. We show that transformed vacuum (boundary state) is given in terms of tau-functions of dispersionless KP (Toda) hierarchies. Applications of this approach to string field theory is considered. We recognize in Neumann coefficients the matrix of second derivatives of tau-function of dispersionless KP and identify surface states with the conformally transformed vacuum of free field theory.Comment: 25 pp, LaTeX, reference added in the Section 3.

No Dynamics in the Extremal Kerr Throat

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.Comment: 42 pages, 3 figures. v3: minor clarifications and correction

Prospects for e+e- physics at Frascati between the phi and the psi

We present a detailed study, done in the framework of the INFN 2006 Roadmap, of the prospects for e+e- physics at the Frascati National Laboratories. The physics case for an e+e- collider running at high luminosity at the phi resonance energy and also reaching a maximum center of mass energy of 2.5 GeV is discussed, together with the specific aspects of a very high luminosity tau-charm factory. Subjects connected to Kaon decay physics are not discussed here, being part of another INFN Roadmap working group. The significance of the project and the impact on INFN are also discussed. All the documentation related to the activities of the working group can be found in http://www.roma1.infn.it/people/bini/roadmap.html.Comment: INFN Roadmap Report: 86 pages, 25 figures, 9 table

Direct Products in Communication Complexity

We give exponentially small upper bounds on the success probability for computing the direct product of any function over any distribution using a communication protocol. Let suc(µ, f, C) denote the maximum success probability of a 2-party communication protocol for computing the boolean function f(x, y) with C bits of communication, when the inputs (x, y) are drawn from the distribution µ. Let µ n be the product distribution on n inputs and f n denote the function that computes n copies of f on these inputs. We prove that if T log 3/2 T ≪ (C − 1) √ n and suc(µ, f, C) < 2 3, then suc(µn, f n, T) ≤ exp(−Ω(n)). When µ is a product distribution, we prove a nearly optimal result: as long as T log 2 T ≪ Cn, we must have suc(µ n, f n, T) ≤ exp(−Ω(n)).