Extended modular operad

This paper is a sequel to [LoMa] where moduli spaces of painted stable curves were introduced and studied. We define the extended modular operad of genus zero, algebras over this operad, and study the formal differential geometric structures related to these algebras: pencils of flat connections and Frobenius manifolds without metric. We focus here on the combinatorial aspects of the picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional references and minor change

Tautological relations in Hodge field theory

We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov-Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof.Comment: 35 page

On the Length of the Relaxation Zone of Ionization Behind a Strong Shock Wave Front in the Air

Relaxation zone behind strong shock wave front in ai

On First Order Formalism in String Theory

We consider the first order formalism in string theory, providing a new off-shell description of the nontrivial backgrounds around an "infinite metric". The OPE of the vertex operators, corresponding to the background fields in some "twistor representation", and conditions of conformal invariance results in the quadratic equation for the background fields, which appears to be equivalent to the Einstein equations with a Kalb-Ramond B-field and a dilaton. Using a new representation for the Einstein equations with B-field and dilaton we find a new class of solutions including the plane waves for metric (graviton) and the B-field. We discuss the properties of these background equations and main features of the BRST operator in this approach.Comment: LaTeX2e, 18 pages, Phys. Lett. B, in press, corrected typo

N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N=2 superalgebra we found paves the way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in {\bar Q_L, Q_R}.Comment: 21 pages, Latex, 1 eps figure. Two important references adde

Ultrabroad-bandwidth multifrequency Raman generation

We report on the modeling of transient stimulated rotational Raman scattering in H2 gas. We predict a multifrequency output, spanning a bandwidth greater than the pump frequency, that may be generated without any significant delay with respect to the pump pulses. The roles of dispersion and transiency are quantified