15,612 research outputs found

### Three Dimensional Topological Field Theory induced from Generalized Complex Structure

We construct a three-dimensional topological sigma model which is induced
from a generalized complex structure on a target generalized complex manifold.
This model is constructed from maps from a three-dimensional manifold $X$ to an
arbitrary generalized complex manifold $M$. The theory is invariant under the
diffeomorphism on the world volume and the $b$-transformation on the
generalized complex structure. Moreover the model is manifestly invariant under
the mirror symmetry. We derive from this model the Zucchini's two dimensional
topological sigma model with a generalized complex structure as a boundary
action on $\partial X$. As a special case, we obtain three dimensional
realization of a WZ-Poisson manifold.Comment: 18 page

### Couplings between a collection of BF models and a set of three-form gauge fields

Consistent interactions that can be added to a free, Abelian gauge theory
comprising a collection of BF models and a set of three-form gauge fields are
constructed from the deformation of the solution to the master equation based
on specific cohomological techniques. Under the hypotheses of smooth, local, PT
invariant, Lorentz covariant, and Poincare invariant interactions, supplemented
with the requirement on the preservation of the number of derivatives on each
field with respect to the free theory, we obtain that the deformation procedure
modifies the Lagrangian action, the gauge transformations as well as the
accompanying algebra.Comment: 17 page

### AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz-
Zaboronsky superfield formalism using the language of graded manifolds. As a
main illustarting example, to every Courant algebroid structure we associate
canonically a three-dimensional topological sigma-model. Using the AKSZ
formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon
200

### 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

### The Functional Integral for a Free Particle on a Half-Plane

A free non-relativistic particle moving in two dimensions on a half-plane can
be described by self-adjoint Hamiltonians characterized by boundary conditions
imposed on the systems. The most general boundary condition is parameterized in
terms of the elements of an infinite-dimensional matrix. We construct the
Brownian functional integral for each of these self-adjoint Hamiltonians.
Non-local boundary conditions are implemented by allowing the paths striking
the boundary to jump to other locations on the boundary. Analytic continuation
in time results in the Green's functions of the Schrodinger equation satisfying
the boundary condition characterizing the self-adjoint Hamiltonian.Comment: 16 page

### An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in
two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case
that the generalized complex structuredepends on only a symplectic structure.
Our new model is $B$ model in the case that the generalized complex structure
depends on only a complex structure.Comment: 29 pages, typos and references correcte

### Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

The algebraic and geometric structures of deformations are analyzed
concerning topological field theories of Schwarz type by means of the
Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in
three dimensions induces the Courant algebroid structure on the target space as
a sigma model. Deformations of BF theories in $n$ dimensions are also analyzed.
Two dimensional deformed BF theory induces the Poisson structure and three
dimensional deformed BF theory induces the Courant algebroid structure on the
target space as a sigma model. The deformations of BF theories in $n$
dimensions induce the structures of Batalin-Vilkovisky algebras on the target
space.Comment: 25 page

### High field superconducting phase diagrams including Fulde-Ferrell-Larkin-Ovchinnikov vortex states

Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov
(FFLO) vortex state in the heavy fermion material CeCoIn5 in fields {\it
perpendicular} to the superconducting planes (${\bf H} \parallel c$),
superconducting phase diagrams including an FFLO state of quasi two-dimensional
(Q2D) superconductors are systematically studied. In the clean {\it limit}, the
high field superconducting state in the low temperature limit should be not the
FFLO state modulating along ${\bf H}$, appeared in CeCoIn5 in both ${\bf H}
\parallel c$ and ${\bf H} \perp c$, but a different vortex state with a
modulation, induced by the paramagnetism, perpendicular to the field. It is
found that the presence of weak impurities is the origin of the absence in
CeCoIn5 of the latter state and leads to the ${\bf H} \parallel c$ phase
diagram, as seen in CeCoIn5, {\it apparently} different in character from that
in ${\bf H} \perp c$.Comment: A reference was updated. To appear in Phys. Rev.

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