756 research outputs found
Spinorial cohomology and maximally supersymmetric theories
Fields in supersymmetric gauge theories may be seen as elements in a
spinorial cohomology. We elaborate on this subject, specialising to maximally
supersymmetric theories, where the superspace Bianchi identities, after
suitable conventional constraints are imposed, put the theories on shell. In
these cases, the spinorial cohomologies describe in a unified manner gauge
transformations, fields and possible deformations of the models, e.g.
string-related corrections in an alpha' expansion. Explicit cohomologies are
calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor
multiplet in D=6 and for supergravity in D=11, in the latter case from the
point of view of both the super-vielbein and the super-3-form potential. The
techniques may shed light on some questions concerning the alpha'-corrected
effective theories, and result in better understanding of the role of the
3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde
U-duality covariant membranes
We outline a formulation of membrane dynamics in D=8 which is fully covariant
under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to
fields in the eight-dimensional supergravity, which is constructed through
Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an
SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric
fluxes determine the membrane charges, and are conjectured to provide an
interpretation of the variables occurring in the minimal representation of
E_{6(6)} which appears in the context of automorphic membranes. We solve the
relevant equations for the action for a restricted class of supergravity
backgrounds. Some comments are made on supersymmetry and lower dimensions.Comment: LaTeX, 21 pages. v2: Minor changes in text, correction of a sign. v3:
some changes in text, a sign convention changed; version to appear in JHE
11D supergravity at
We compute certain spinorial cohomology groups controlling possible
supersymmetric deformations of eleven-dimensional supergravity up to order
in the Planck length. At and the spinorial
cohomology groups are trivial and therefore the theory cannot be deformed
supersymmetrically. At the corresponding spinorial cohomology
group is generated by a nontrivial element. On an eleven-dimensional manifold
such that , this element corresponds to a supersymmetric
deformation of the theory, which can only be redefined away at the cost of
shifting the quantization condition of the four-form field strength.Comment: 10 pages, 1 figure. v2: references adde
Pure Spinors and D=6 Super-Yang-Mills
Pure spinor cohomology has been used to describe maximally supersymmetric
theories, like D=10 super-Yang-Mills and D=11 supergravity. Supersymmetry
closes on-shell in such theories, and the fields in the cohomology
automatically satisfy the equations of motion. In this paper, we investigate
the corresponding structure in a model with off-shell supersymmetry, N=1
super-Yang-Mills theory in D=6. Here, fields and antifields are obtained as
cohomologies in different complexes with respect to the BRST operator Q. It
turns out to be natural to enlarge the pure spinor space with additional
bosonic variables, subject to some constraints generalising the pure spinor
condition, in order to accommodate the different supermultiplets in the same
generalised pure spinor wave-function. We construct another BRST operator, s,
acting in the cohomology of Q, whose cohomology implies the equations of
motion. We comment on the possible use of similar approaches in other models.Comment: 11 pp, 3 figs, plain te
Towards a manifestly supersymmetric action for 11-dimensional supergravity
We investigate the possibility of writing a manifestly supersymmetric action
for 11-dimensional supergravity. The construction involves an explicit relation
between the fields in the super-vielbein and the super-3-form, and uses
non-minimal pure spinors. A simple cubic interaction term for a single scalar
superfield is found.Comment: 22 pp., plain tex. v2: references adde
A Note on Topological M5-branes and String-Fivebrane Duality
We derive the stability conditions for the M5-brane in topological M-theory
using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is
necessarily non-vanishing, as is the case also for the 2-form field strengths
on coisotropic branes in topological string theory. It is demonstrated that the
self-duality is consistent with the stability conditions, which are solved
locally in terms of a tensor in the representation 6 of SU(3) in G_2. The
double dimensional reduction of the M5-brane is the D4-brane, and its direct
reduction is an NS5-brane. We show that the equation of motion for the 3-form
on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer
equation, providing support for a string-fivebrane duality in topological
string theory.Comment: 11 pp, plain te
An action for the super-5-brane in D=11 supergravity
An alternative path is taken for deriving an action for the supersymmetric
5-brane in 11 dimensions. Selfduality does not follow from the action, but is
consistent with the equations of motion for arbitrary supergravity backgrounds.
The action involves a 2-form as well as a 5-form world-volume potential;
inclusion of the latter makes the action, as well as the non-linear selfduality
relation for the 3-form field strength, polynomial. The requirement of
invariance under kappa-transformations determines the form of the selfduality
relation, as well as the action. The formulation is shown to be equivalent to
earlier formulations of 5-brane dynamics.Comment: plain tex, 8pp. Essential correction to the selfduality equation.
Added paragraph showing equivalence to other formulation
The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
We solve the superspace Bianchi identities for ten-dimensional supersymmetric
Yang-Mills theory without imposing any kind of constraints apart from the
standard conventional one. In this way we obtain a set of algebraic conditions
on certain fields which in the on-shell theory are constructed as composite
ones out of the physical fields. These conditions must hence be satisfied by
any kind of theory in ten dimensions invariant under supersymmetry and some,
abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory
(as well as the fields) are identified as elements of a certain spinorial
cohomology, giving control over field redefinitions and the distinction between
physically relevant higher-order corrections and those removable by field
redefinitions. The conditions derived severely constrain theories involving
F^2-level terms plus higher-order corrections, as for instance those derived
from open strings as effective gauge theories on D-branes.Comment: plain tex, 18 pp., 3 fig
D=3, N=8 conformal supergravity and the Dragon window
We give a superspace description of D=3, N=8 supergravity. The formulation is
off-shell in the sense that the equations of motion are not implied by the
superspace constraints (but an action principle is not given). The multiplet
structure is unconventional, which we connect to the existence of a "Dragon
window", that is modules occurring in the supercurvature but not in the
supertorsion. According to Dragon's theorem this cannot happen above three
dimensions. We clarify the relevance of this window for going on the conformal
shell, and discuss some aspects of coupling to conformal matter.Comment: plain tex, 24 pp v2: minor change
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