2,887 research outputs found
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
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
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
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
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
Supergravity and the Knitting of the Kalb--Ramond Two-Form in Eight-Dimensional Topological Gravity
Topological euclidean gravity is built in eight dimensions for manifolds with
holonomy. In a previous work, we considered the
construction of an eight-dimensional topological theory describing the graviton
and one graviphoton. Here we solve the question of determining a topological
model for the combined system of a metric and a Kalb--Ramond two-form gauge
field. We then recover the complete supergravity theory in a twisted
form. We observe that the generalized self-duality conditions of our model
correspond to the octonionic string equations.Comment: 17 page
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
Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries
After adding 7 auxiliary scalars to the d=10 super-Yang-Mills action, 9 of
the 16 supersymmetries close off-shell. In this paper, these 9 supersymmetry
generators are related by dimensional reduction to scalar and vector
topological symmetry in =2 d=8 twisted super-Yang-Mills. Furthermore, a
gauge-invariant superspace action is constructed for d=10 super-Yang-Mills
where the superfields depend on 9 anticommuting theta variables.Comment: 15 page
Worldsheets with Extended Supersymmetry
We determine the equations which govern the gauge symmetries of worldsheets
with local supersymmetry of arbitrary rank , and their possible
anomalies. Both classical and ghost conformally invariant multiplets of the
left or right sector are assembled into the components of a single
-superfield. The component with ghost number zero of this superfield is
the -supersymmetric generalization of the Beltrami differential. In a
Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of
Riemann surfaces coupled to local supersymmetry of rank . It is also the
source of all linear superconformal currents derived from ordinary operator
product techniques. The interconnection between BRST invariant actions with
different values of , and their possible link to topological
2D-gravity coupled to topological sigma models, are shown by straightforward
algebraic considerations.Comment: 15 pages, Latex. A section on the connection to topological action is
adde
Reconstruction of N=1 supersymmetry from topological symmetry
The scalar and vector topological Yang-Mills symmetries on Calabi-Yau
manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1
supersymmetry, which fully determine the supersymmetric actions up to twist.
For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory
can be reconstructed in this way. A superpotential can be introduced for the
matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold,
the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting
these results together with those already known for the D=4,8 N=2 cases, we
conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are
determined from topological symmetry on special manifolds.Comment: 13 page
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