120 research outputs found
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
(-algebras) by closed strings (-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
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 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.
Noncommutative homotopy algebras associated with open strings
We discuss general properties of -algebras and their applications
to the theory of open strings. The properties of cyclicity for
-algebras are examined in detail. We prove the decomposition theorem,
which is a stronger version of the minimal model theorem, for
-algebras and cyclic -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 -isomorphic to each other. The
same results hold for classical closed string field theories, whose algebraic
structure is governed by cyclic -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 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
Invariants from classical field theory
We introduce a method that generates invariant functions from perturbative
classical field theories depending on external parameters. Applying our methods
to several field theories such as abelian BF, Chern-Simons and 2-dimensional
Yang-Mills theory, we obtain, respectively, the linking number for embedded
submanifolds in compact varieties, the Gauss' and the second Milnor's invariant
for links in S^3, and invariants under area-preserving diffeomorphisms for
configurations of immersed planar curves.Comment: 20 pages, 1 figure, to appear in J. Math. Phy
On the integral cohomology of smooth toric varieties
Let be a smooth, not necessarily compact toric variety. We show
that a certain complex, defined in terms of the fan , computes the
integral cohomology of , 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
is formal.Comment: 10 page
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