523 research outputs found
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
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
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
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
Calculations of the Local Density of States for some Simple Systems
A recently proposed convolution technique for the calculation of local
density of states is described more thouroughly and new results of its
application are presented. For separable systems the exposed method allows to
construct the ldos for a higher dimensionality out of lower dimensional parts.
Some practical and theoretical aspects of this approach are also discussed.Comment: 5 pages, 3 figure
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