910 research outputs found
Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes
We investigate the generic 3D topological field theory within AKSZ-BV
framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly
cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue
that the perturbative partition function gives rise to secondary characteristic
classes. We investigate a toy model which is an odd analogue of Chern-Simons
theory, and we give some explicit computation of two point functions and show
that its perturbation theory is identical to the Chern-Simons theory. We give
concrete example of the homomorphism taking Lie algebra cocycles to
Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in
this light.Comment: 52 page
Supersymmetry and localization
We study conditions under which an odd symmetry of the integrand leads to
localization of the corresponding integral over a (super)manifold. We also show
that in many cases these conditions guarantee exactness of the stationary phase
approximation of such integrals.Comment: 16 pages, LATE
QP-Structures of Degree 3 and 4D Topological Field Theory
A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structure
of degree 3 gives rise to Lie algebroids up to homotopy and its algebraic and
geometric structure is analyzed. A new algebroid is constructed, which derives
a new topological field theory in 4 dimensions by the AKSZ construction.Comment: 17 pages, Some errors and typos have been correcte
Quantization and holomorphic anomaly
We study wave functions of B-model on a Calabi-Yau threefold in various
polarizations.Comment: 15 page
Classical BV theories on manifolds with boundary
In this paper we extend the classical BV framework to gauge theories on
spacetime manifolds with boundary. In particular, we connect the BV
construction in the bulk with the BFV construction on the boundary and we
develop its extension to strata of higher codimension in the case of manifolds
with corners. We present several examples including electrodynamics, Yang-Mills
theory and topological field theories coming from the AKSZ construction, in
particular, the Chern-Simons theory, the theory, and the Poisson sigma
model. This paper is the first step towards developing the perturbative
quantization of such theories on manifolds with boundary in a way consistent
with gluing.Comment: The second version has many typos corrected, references added. Some
typos are probably still there, in particular, signs in examples. In the
third version more typoes are corrected and the exposition is slightly
change
Superfield algorithm for higher order gauge field theories
We propose an algorithm for the construction of higher order gauge field
theories from a superfield formulation within the Batalin-Vilkovisky formalism.
This is a generalization of the superfield algorithm recently considered by
Batalin and Marnelius. This generalization seems to allow for non-topological
gauge field theories as well as alternative representations of topological
ones. A five dimensional non-abelian Chern-Simons theory and a topological
Yang-Mills theory are treated as examples.Comment: 17 pages in LaTeX, improved text, published versio
More on core instabilities of magnetic monopoles
In this paper we present new results on the core instability of the 't Hooft
Polyakov monopoles we reported on before. This instability, where the spherical
core decays in a toroidal one, typically occurs in models in which charge
conjugation is gauged. In this paper we also discuss a third conceivable
configuration denoted as ``split core'', which brings us to some details of the
numerical methods we employed. We argue that a core instability of 't Hooft
Polyakov type monopoles is quite a generic feature of models with charged Higgs
particles.Comment: Latex, 15 pages, 6 figures; published versio
On symmetries of Chern-Simons and BF topological theories
We describe constructing solutions of the field equations of Chern-Simons and
topological BF theories in terms of deformation theory of locally constant
(flat) bundles. Maps of flat connections into one another (dressing
transformations) are considered. A method of calculating (nonlocal) dressing
symmetries in Chern-Simons and topological BF theories is formulated
BFV-complex and higher homotopy structures
We present a connection between the BFV-complex (abbreviation for
Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie
algebroid associated to a coisotropic submanifold of a Poisson manifold. We
prove that the latter structure can be derived from the BFV-complex by means of
homotopy transfer along contractions. Consequently the BFV-complex and the
strong homotopy Lie algebroid structure are quasi-isomorphic and
control the same formal deformation problem.
However there is a gap between the non-formal information encoded in the
BFV-complex and in the strong homotopy Lie algebroid respectively. We prove
that there is a one-to-one correspondence between coisotropic submanifolds
given by graphs of sections and equivalence classes of normalized Maurer-Cartan
elemens of the BFV-complex. This does not hold if one uses the strong homotopy
Lie algebroid instead.Comment: 50 pages, 6 figures; version 4 is heavily revised and extende
A supergeometric approach to Poisson reduction
This work introduces a unified approach to the reduction of Poisson manifolds
using their description by graded symplectic manifolds. This yields a
generalization of the classical Poisson reduction by distributions
(Marsden-Ratiu reduction). Further it allows one to construct actions of strict
Lie 2-groups and to describe the corresponding reductions.Comment: 40 pages. Final version accepted for publicatio
- …