73 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
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 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 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
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.
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