18,606 research outputs found
Towards an exact frame formulation of conformal higher spins in three dimensions
In this note we discuss some aspects of the frame formulation of conformal
higher spins in three dimensions. We give some exact formulae for the coupled
spin two - spin three part of the full higher spin theory and propose a star
product Lagrangian for all spins from two and up. Since there is no consistent
Lagrangian formulation based on the Poisson bracket we start the construction
from the field equations in this approximation of the star product. The higher
spin algebra is then realized in terms of classical variables which leads to
certain important simplifications that we take advantage of. The suggested
structure of the all-spin Lagrangian given here is, however, obtained using an
expansion of the star product beyond the Poisson bracket in terms of
multi-commutators and the Lagrangian should be viewed as a starting point for
the derivation of the full theory based on a star product. How to do this is
explained as well as how to include the coupling to scalar fields. We also
comment on the AdS/CFT relation to four dimensions.Comment: 18 pages, v2: misprints corrected, an appendix, footnotes and some
clarifying remarks added, 21 page
On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
We propose field equations for the conformal higher spin system in three
dimensions coupled to a conformal scalar field with a sixth order potential.
Both the higher spin equation and the unfolded equation for the scalar field
have source terms and are based on a conformal higher spin algebra which we
treat as an expansion in multi-commutators. Explicit expressions for the source
terms are suggested and subjected to some simple tests. We also discuss a
cascading relation between the Chern-Simons action for the higher spin gauge
theory and an action containing a term for each spin that generalizes the spin
2 Chern-Simons action in terms of the spin connection expressed in terms of the
frame field. This cascading property is demonstrated in the free theory for
spin 3 but should work also in the complete higher spin theory.Comment: v2: 20 pages, misprints corrected, footnotes 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
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
On relating multiple M2 and D2-branes
Due to the difficulties of finding superconformal Lagrangian theories for
multiple M2-branes, we will in this paper instead focus on the field equations.
By relaxing the requirement of a Lagrangian formulation we can explore the
possibility of having structure constants satisfying the
fundamental identity but which are not totally antisymmetric. We exemplify this
discussion by making use of an explicit choice of a non-antisymmetric
constructed from the Lie algebra structure constants
of an arbitrary gauge group. Although this choice of does not
admit an obvious Lagrangian description, it does reproduce the correct SYM
theory for a stack of D2-branes to leading order in upon
reduction and, moreover, it sheds new light on the centre of mass coordinates
for multiple M2-branes.Comment: 9 pages, references added and statements concerning the fundamental
identity revise
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
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
Off-shell structure of twisted (2,0) theory
A -exact off-shell action is constructed for twisted abelian (2,0) theory
on a Lorentzian six-manifold of the form , where is
a flat two-manifold and is a general Euclidean four-manifold. The
properties of this formulation, which is obtained by introducing two auxiliary
fields, can be summarised by a commutative diagram where the Lagrangian and its
stress-tensor arise from the -variation of two fermionic quantities and
. This completes and extends the analysis in
[arXiv:1311.3300].Comment: 15 pages, 2 figure
Manifestly supersymmetric M-theory
In this paper, the low-energy effective dynamics of M-theory,
eleven-dimensional supergravity, is taken off-shell in a manifestly
supersymmetric formulation. We show that a previously proposed relaxation of
the superspace torsion constraints does indeed accommodate a current
supermultiplet which lifts the equations of motion corresponding to the
ordinary second order derivative supergravity lagrangian. Whether the auxiliary
fields obtained this way can be used to construct an off-shell lagrangian is
not yet known. We comment on the relation and application of this completely
general formalism to higher-derivative (R^4) corrections. Some details of the
calculation are saved for a later publication.Comment: 13 pages, plain tex. v2: minor changes, one ref. adde
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