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

Anticommutativity Equation in Topological Quantum Mechanics

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological corellators in this theory. We prove that the generating function $\mathcal{F}$ for thus corellators satisfies the anticommutativity equation $(\mathcal{D}- \mathcal{F})^2=0$. We show that the commutativity equation $[dB,dB]=0$ could be considered as a special case of the anticommutativity equation.Comment: 6 pages, no figures, Late

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

Simulation of oxygen dissociation on a six-dimensional O4 potential energy surface

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143058/1/6.2017-3487.pd

Single State Supermultiplet in 1+1 Dimensions

We consider multiplet shortening for BPS solitons in N=1 two-dimensional models. Examples of the single-state multiplets were established previously in N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the fermion parity $(-1)^F$ due to boundary effects. This implies the disappearance of the boson-fermion classification resulting in abnormal statistics. We discuss an appropriate index that counts such short multiplets. A broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space is considered. Our index turns out to be related to the index of the Dirac operator on the soliton reduced moduli space (the moduli space is reduced by factoring out the translational modulus). The index vanishes in most cases implying the absence of shortening. In particular, it vanishes when there are only two critical points on the compact target space and the reduced moduli space has nonvanishing dimension. We also generalize the anomaly in the central charge to take into account the target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds. M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The paper is drastically revised compared to the first version. We add sections treating the following issues: (i) a new index counting one-state supermultiplets; (ii) analysis of hybrid models of general type; (iii) generalization of the anomaly in the central charge accounting for the target space metri

Mirror symmetry in two steps: A-I-B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second theory is an intermediate model, which we call the I-model. The equivalence between the A-model and the I-model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T-duality. On the other hand, the I-model is closely related to the twisted Landau-Ginzburg model (the B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is realized in two steps, via the I-model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I-model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Comment: 50 pages; revised versio