Open-closed homotopy algebra in mathematical physics

In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures ($A_\infty$-algebras) by closed strings ($L_\infty$-algebras).Comment: 38 pages, 4 figures; v2: published versio

Irreducible Hamiltonian BRST approach to topologically coupled abelian forms

An irreducible Hamiltonian BRST approach to topologically coupled p- and (p+1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST point of view to the original redundant theory. The irreducible path integral can be brought to a manifestly Lorentz covariant form.Comment: 29 pages, LaTeX 2.0

A Note on "Irreducible" p-Form Gauge Theories with Stueckelberg Coupling

p-form gauge theories with Stueckelberg coupling are quantized in an irreducible antifield-BRST way. As a consequence, neither the ghosts of ghosts nor their antifields appear. Some irreducible gauge conditions are inferred naturally within our formalism. In the end we briefly discuss the interacting case.Comment: 10 pag, latex 2.09, no figure

Noncommutative homotopy algebras associated with open strings

We discuss general properties of $A_\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\infty$-algebras and cyclic $A_\infty$-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic $A_\infty$-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic $L_\infty$-algebras.Comment: 92 pages, 16 figuers; based on Ph.D thesis submitted to Graduate School of Mathematical Sciences, Univ. of Tokyo on January, 2003; v2: explanation improved, references added, published versio

Irreducible Hamiltonian BRST symmetry for reducible first-class systems

An irreducible Hamiltonian BRST quantization method for reducible first-class systems is proposed. The general theory is illustrated on a two-stage reducible model, the link with the standard reducible BRST treatment being also emphasized.Comment: Latex 2.09, 23 pages, to appear in Int. J. Mod. Phys.

Irreducible Hamiltonian approach to the Freedman-Townsend model

The irreducible BRST symmetry for the Freedman-Townsend model is derived. The comparison with the standard reducible approach is also addressed.Comment: 18 pages, LaTeX 2.0

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.Comment: 35 page

Irreducible antifield-BRST approach to reducible gauge theories

An irreducible antifield BRST quantization method for reducible gauge theories is proposed. The general formalism is illustrated in the case of the Freedman-Townsend model.Comment: 19 pages, LaTeX 2.0

On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page

Lagrangian Sp(3) BRST symmetry for irreducible gauge theories

The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket-antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.Comment: LaTeX 2e, 42 pages, to appear in Int. J. Mod. Phys.