Homotopy Relations for Topological VOA

We consider a parameter-dependent version of the homotopy associative part of the Lian-Zuckerman homotopy algebra and provide the interpretation of multilinear operations of this algebra in terms of integrals over certain polytopes. We explicitly prove the pentagon relation up to homotopy and propose a construction of higher operations.Comment: 15 pages, 1 figure, typos correcte

QED2+1_{2+1} with Nonzero Fermion Density and Quantum Hall Effect

A general expression for the conductivity in the QED$_{2+1}$ with nonzero fermion density in the uniform magnetic field is derived. It is shown that the conductivity is entirely determined by the Chern-Simons coefficient: $\sigma_{ij}=\varepsilon_{ij}~{\cal C}$ and is a step-function of the chemical potential and the magnetic field.Comment: 8 pages, LaTeX; FIAN/TD/94-0

Induced Magnetic Field in a Finite Fermion Density Maxwell QED2+1_{2+1}

We are studying finite fermion density states in Maxwell QED$_{2+1}$ with external magnetic field. It is shown that at any fermion density the energy of some magnetized states may be less than that of the state with the same density, but no magnetic field. Magnetized states are described by the effective Maxwell-Chern-Simons QED$_{2+1}$ Lagrangian with gauge field mass proportional to the number of filled Landau levels.Comment: 9 pages, 3 LaTeX figures included; 1 figure change

BV Yang-Mills as a Homotopy Chern-Simons via SFT

We show explicitly how BV Yang-Mills action emerges as a homotopy generalization of Chern-Simons theory from the algebraic constructions arising from String Field Theory.Comment: LaTeX2e, 22 pages, minor revisions, typos corrected, references added, Int. J. Mod. Physics A, published versio