239 research outputs found
Higher Poincare Lemma and Integrability
We prove the non-abelian Poincare lemma in higher gauge theory in two
different ways. The first method uses a result by Jacobowitz which states
solvability conditions for differential equations of a certain type. The second
method extends a proof by Voronov and yields the explicit gauge parameters
connecting a flat local connective structure to the trivial one. Finally, we
show how higher flatness appears as a necessary integrability condition of a
linear system which featured in recently developed twistor descriptions of
higher gauge theories.Comment: 1+21 pages, presentation streamlined, section on integrability for
higher linear systems significantly improved, published versio
A Lorentzian analog for Hausdorff dimension and measure
We define a one-parameter family of canonical volume measures on Lorentzian
(pre-)length spaces. In the Lorentzian setting, this allows us to define a
geometric dimension - akin to the Hausdorff dimension for metric spaces - that
distinguishes between e.g. spacelike and null subspaces of Minkowski spacetime.
The volume measure corresponding to its geometric dimension gives a natural
reference measure on a synthetic or limiting spacetime, and allows us to define
what it means for such a spacetime to be collapsed (in analogy with metric
measure geometry and the theory of Riemannian Ricci limit spaces). As a crucial
tool we introduce a doubling condition for causal diamonds and a notion of
causal doubling measures. Moreover, applications to continuous spacetimes and
connections to synthetic timelike curvature bounds are given.Comment: 45 pages, 4 figures; v2: minor improvement
Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory
We analyze the gauge structure of a recently proposed superconformal field
theory in six dimensions. We find that this structure amounts to a weak
Courant-Dorfman algebra, which, in turn, can be interpreted as a strong
homotopy Lie algebra. This suggests that the superconformal field theory is
closely related to higher gauge theory, describing the parallel transport of
extended objects. Indeed we find that, under certain restrictions, the field
content and gauge transformations reduce to those of higher gauge theory. We
also present a number of interesting examples of admissible gauge structures
such as the structure Lie 2-algebra of an abelian gerbe, differential crossed
modules, the 3-algebras of M2-brane models and string Lie 2-algebras.Comment: 31+1 pages, presentation slightly improved, version published in JM
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
Non-Abelian Tensor Multiplet Equations from Twistor Space
We establish a Penrose-Ward transform yielding a bijection between
holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual
tensor fields on six-dimensional flat space-time. Extending the twistor space
to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0)
supersymmetric non-Abelian constraint equations containing the tensor
multiplet. We also demonstrate how this construction leads to constraint
equations for non-Abelian supersymmetric self-dual strings.Comment: v3: 23 pages, revised version published in Commun. Math. Phy
A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
Super twistor space admits a certain (super) complex structure deformation
that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends
on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in
twistor string theory this deformation corresponds to augmenting N=4 super
Yang-Mills theory by a mass term for the left-chirality spinors. In this paper
we analyze this proposal in more detail. We calculate 4-particle scattering
amplitudes of fermions, gluons and scalars and show that they are supported on
holomorphic curves in the deformed twistor space.Comment: 52 pages, 15 figure
Multiple M2-branes and Generalized 3-Lie algebras
We propose a generalization of the Bagger-Lambert-Gustavsson action as a
candidate for the description of an arbitrary number of M2-branes. The action
is formulated in terms of N=2 superfields in three dimensions and corresponds
to an extension of the usual superfield formulation of Chern-Simons matter
theories. Demanding gauge invariance of the resulting theory does not imply the
total antisymmetry of the underlying 3-Lie algebra structure constants. We
relax this condition and propose a class of examples for these generalized
3-Lie algebras. We also discuss how to associate various ordinary Lie algebras.Comment: 1+19 pages, version published in Phys. Rev.
Adding flavour to twistor strings
Twistor string theory is known to describe a wide variety of field theories
at tree-level and has proved extremely useful in making substantial progress in
perturbative gauge theory. We explore the twistor dual description of a class
of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding
'flavour' branes to the topological B-model on super-twistor space and comment
on the appearance of these objects. Evidence for the correspondence is provided
by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical
Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3:
Typos correcte
Fuzzy Torus via q-Parafermion
We note that the recently introduced fuzzy torus can be regarded as a
q-deformed parafermion. Based on this picture, classification of the Hermitian
representations of the fuzzy torus is carried out. The result involves
Fock-type representations and new finite dimensional representations for q
being a root of unity as well as already known finite dimensional ones.Comment: 12pages, no figur
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