420 research outputs found
On the E10/Massive Type IIA Supergravity Correspondence
In this paper we investigate in detail the correspondence between E10 and
Romans' massive deformation of type IIA supergravity. We analyse the dynamics
of a non-linear sigma model for a spinning particle on the coset space
E10/K(E10) and show that it reproduces the dynamics of the bosonic as well as
the fermionic sector of the massive IIA theory, within the standard truncation.
The mass deformation parameter corresponds to a generator of E10 outside the
realm of the generators entering the usual D=11 analysis, and is naturally
included without any deformation of the coset model for E10/K(E10). Our
analysis thus provides a dynamical unification of the massless and massive
versions of type IIA supergravity inside E10. We discuss a number of additional
and general features of relevance in the analysis of any deformed supergravity
in the correspondence to Kac-Moody algebras, including recently studied
deformations where the trombone symmetry is gauged.Comment: 68 pages, including 5 appendices, 5 figures. v2: Typos corrected,
published version. v3:Title correcte
Differential-Algebraic Equations
Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed
On the Lie-algebraic origin of metric 3-algebras
Since the pioneering work of Bagger-Lambert and Gustavsson, there has been a
proliferation of three-dimensional superconformal Chern-Simons theories whose
main ingredient is a metric 3-algebra. On the other hand, many of these
theories have been shown to allow for a reformulation in terms of standard
gauge theory coupled to matter, where the 3-algebra does not appear explicitly.
In this paper we reconcile these two sets of results by pointing out the
Lie-algebraic origin of some metric 3-algebras, including those which have
already appeared in three-dimensional superconformal Chern-Simons theories.
More precisely, we show that the real 3-algebras of Cherkis-Saemann, which
include the metric Lie 3-algebras as a special case, and the hermitian
3-algebras of Bagger-Lambert can be constructed from pairs consisting of a
metric real Lie algebra and a faithful (real or complex, respectively) unitary
representation. This construction generalises and we will see how to construct
many kinds of metric 3-algebras from pairs consisting of a real metric Lie
algebra and a faithful (real, complex or quaternionic) unitary representation.
In the real case, these 3-algebras are precisely the Cherkis-Saemann algebras,
which are then completely characterised in terms of this data. In the complex
and quaternionic cases, they constitute generalisations of the Bagger-Lambert
hermitian 3-algebras and anti-Lie triple systems, respectively, which underlie
N=6 and N=5 superconformal Chern-Simons theories, respectively. In the process
we rederive the relation between certain types of complex 3-algebras and metric
Lie superalgebras.Comment: 29 pages (v4: really final version to appear in CMP. Example 7 has
been improved.
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