31 research outputs found
One-dimensional Chern-Simons theory
We study a one-dimensional toy version of the Chern-Simons theory. We
construct its simplicial version which comprises features of a low-energy
effective gauge theory and of a topological quantum field theory in the sense
of Atiyah.Comment: 37 page
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
Electron spin evolution induced by interaction with nuclei in a quantum dot
We study the decoherence of a single electron spin in an isolated quantum dot
induced by hyperfine interaction with nuclei for times smaller than the nuclear
spin relaxation time. The decay is caused by the spatial variation of the
electron envelope wave function within the dot, leading to a non-uniform
hyperfine coupling . We show that the usual treatment of the problem based
on the Markovian approximation is impossible because the correlation time for
the nuclear magnetic field seen by the electron spin is itself determined by
the flip-flop processes.
The decay of the electron spin correlation function is not exponential but
rather power (inverse logarithm) law-like. For polarized nuclei we find an
exact solution and show that the precession amplitude and the decay behavior
can be tuned by the magnetic field. The decay time is given by ,
where is the number of nuclei inside the dot. The amplitude of precession,
reached as a result of the decay, is finite. We show that there is a striking
difference between the decoherence time for a single dot and the dephasing time
for an ensemble of dots.Comment: Revtex, 11 pages, 5 figure
Holomorphic potentials for graded D-branes
We discuss gauge-fixing, propagators and effective potentials for topological
A-brane composites in Calabi-Yau compactifications. This allows for the
construction of a holomorphic potential describing the low-energy dynamics of
such systems, which generalizes the superpotentials known from the ungraded
case. Upon using results of homotopy algebra, we show that the string field and
low energy descriptions of the moduli space agree, and that the deformations of
such backgrounds are described by a certain extended version of `off-shell
Massey products' associated with flat graded superbundles. As examples, we
consider a class of graded D-brane pairs of unit relative grade. Upon computing
the holomorphic potential, we study their moduli space of composites. In
particular, we give a general proof that such pairs can form acyclic
condensates, and, for a particular case, show that another branch of their
moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure
Cohomological aspects on complex and symplectic manifolds
We discuss how quantitative cohomological informations could provide
qualitative properties on complex and symplectic manifolds. In particular we
focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since
they represent useful tools in studying non K\"ahler geometry. We give an
overview on the comparisons among the dimensions of the cohomology groups that
can be defined and we show how we reach the -lemma
in complex geometry and the Hard-Lefschetz condition in symplectic geometry.
For more details we refer to [6] and [29].Comment: The present paper is a proceeding written on the occasion of the
"INdAM Meeting Complex and Symplectic Geometry" held in Cortona. It is going
to be published on the "Springer INdAM Series
On the Open-Closed B-Model
We study the coupling of the closed string to the open string in the
topological B-model. These couplings can be viewed as gauge invariant
observables in the open string field theory, or as deformations of the
differential graded algebra describing the OSFT. This is interpreted as an
intertwining map from the closed string sector to the deformation (Hochschild)
complex of the open string algebra. By an explicit calculation we show that
this map induces an isomorphism of Gerstenhaber algebras on the level of
cohomology. Reversely, this can be used to derive the closed string from the
open string. We shortly comment on generalizations to other models, such as the
A-model.Comment: LaTeX, 48 pages. Citation adde
The twistor connection and gauge invariance principle
It is shown that the twistor connection of the local twistor theory can be regarded as a gauge field whose Yang-Mills equations are equivalent to Bach equations of gravity. © 1984 Springer-Verlag