164 research outputs found
On Forms with Non-Abelian Charges and Their Dualities
We describe forms with non-Abelian charges. We avoid the use of theories with
flat curvatures by working in the context of topological field theory. We
obtain TQFTs for a form and its dual. We leave open the question of getting
gauges in which the form, or its dual, can be gauged away, in such way that the
model has two dual formulations. We give the example of charged two-forms in
six dimensions.Comment: 11 pages, harvmac fil
Supersymmetry with a Ghost Time
The progress brought to the study of chiral fermions and gauge theories by
quantization methods with a bulk time suggests their usefulness in
supersymmetric theories. Using superspace methods, we show how an explicitly
supersymmetric version of such quantization methods may be given.Comment: 6 page
Four twisted differential operators for the N=4 superconformal algebra
The N=4, d=4 Yang-Mills conformal supersymmetry exhibits a very simple
sub-sector described by four differential operators. The invariance under this
subalgebra is big enough to determine the N=4 theory. Some attempts are done to
interpret these differential operators
N=4 Yang--Mills theory as a complexification of the N=2 theory
A complexification of the twisted theory allows one to determine the
N=4 Yang--Mills theory in its third twist formulation. The imaginary part of
the gauge symmetry is used to eliminate two scalars fields and create gauge
covariant longitudinal components for the imaginary part of the gauge field.
The latter becomes the vector field of the thirdly twisted theory.
Eventually, one gets a one to one correspondence between the fields of both
theories. Analogous complexifications can be done for topological 2d-gravity
and topological sigma models
SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
The N=1,d=10 superYang-Mills action is constructed in a twisted form, using
SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its
off-shell closed twisted scalar supersymmetry operator Q derive from a
Chern-Simons term. The action can be decomposed as the sum of a term in the
cohomology of Q and of a term that is Q-exact. The first term is a fermionic
Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is
related to the second one by a twisted vector supersymmetry with 5 parameters.
The cohomology of Q and some topological observables are defined from descent
equations. In this SU(5)<SO(10)$ invariant decomposition, the N=1, d=10 theory
is determined by only 6 supersymmetry generators, as in the twisted N=4, d=4
theory. There is a superspace with 6 twisted fermionic directions, with
solvable constraints.Comment: 10 page
Going down from a 3-form in 16 dimensions
Group theory indicates the existence of a
invariant self-duality equation for a 3-form in 16 dimensions. It is a signal
for interesting topological field theories, especially on 8-dimensional
manifolds with holonomy group smaller than or equal to Spin(7), with a gauge
symmetry that is SO(8) or SO(7). Dimensional reduction also provides new
supersymmetric theories in 4 and lower dimensions, as well as a model with
gravitational interactions in 8 dimensions, which relies on the octonionic
gravitational self-duality equation.Comment: 14 page
Transmutation of Pure 2-D Supergravity Into Topological 2-D Gravity and Other Conformal Theories
We consider the BRST and superconformal properties of the ghost action of 2-D
supergravity. Using the background spin structure on the worldsheet, we show
that this action can be transformed by canonical field transformations to reach
other conformal models such as the 2-D topological gravity or the chiral models
for which the gauge variation of the action reproduces the left or right
conformal anomaly. Our method consists in using the gravitino and its ghost as
fundamental blocks to build fields with different conformal weights and
statistics. This indicates in particular that the twisting of a conformal model
into another one can be classically interpreted as a change of "field
representation" of the superconformal symmetry.Comment: 20 pages, PAR-LPTHE 92-2
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