Local E(11) and the gauging of the trombone symmetry

Fabio Riccioni

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Local E(11) and the gauging of the trombone symmetry

Fabio Riccioni

High Energy Physics - Theory · Submitted 8 Jan 2010

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The authors' main claim We show the existence of a new type of deformation of the local $E_{11}$ algebra, which corresponds to the gauging of the symmetry under rescaling of the fields.

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What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.41 · mentions code or data availability 0.01.

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In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity. We consider the local $E_{11}$ algebra, that is the algebra obtained enlarging these generators of $E_{11}$ in such a way that the global $E_{11}$ symmetries are promoted to gauge symmetries. These are the gauge symmetries of the corresponding massless maximal supergravity. We show the existence of a new type of deformation of the local $E_{11}$ algebra, which corresponds to the gauging of the symmetry under rescaling of the fields. In particular, we show how the gauged IIA theory of Howe, Lambert and West is obtained from an eleven-dimensional group element that only depends on the eleventh coordinate via a linear rescaling. We then show how this results in ten dimensions in a deformed local $E_{11}$ algebra of a new type.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity.	background 1.00	0.11	0.05	asserted 1.00
s1	We consider the local $E_{11}$ algebra, that is the algebra obtained enlarging these generators of $E_{11}$ in such a way that the global $E_{11}$ symmetries are promoted to gauge symmetries.	contribution 0.82	0.66	0.08	asserted 0.95
s2	These are the gauge symmetries of the corresponding massless maximal supergravity.	interpretation 0.45	0.15	0.09	asserted 1.00
s3	We show the existence of a new type of deformation of the local $E_{11}$ algebra, which corresponds to the gauging of the symmetry under rescaling of the fields.	result 0.61	0.95	0.64	asserted 1.00
s4	In particular, we show how the gauged IIA theory of Howe, Lambert and West is obtained from an eleven-dimensional group element that only depends on the eleventh coordinate via a linear rescaling.	result 0.73	0.79	0.16	asserted 1.00
s5	We then show how this results in ten dimensions in a deformed local $E_{11}$ algebra of a new type.	result 0.92	0.93	0.22	asserted 1.00

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Original abstract

In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity. We consider the local $E_{11}$ algebra, that is the algebra obtained enlarging these generators of $E_{11}$ in such a way that the global $E_{11}$ symmetries are promoted to gauge symmetries. These are the gauge symmetries of the corresponding massless maximal supergravity. We show the existence of a new type of deformation of the local $E_{11}$ algebra, which corresponds to the gauging of the symmetry under rescaling of the fields. In particular, we show how the gauged IIA theory of Howe, Lambert and West is obtained from an eleven-dimensional group element that only depends on the eleventh coordinate via a linear rescaling. We then show how this results in ten dimensions in a deformed local $E_{11}$ algebra of a new type.

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4 arXiv papers cite this in 10 sentences

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Papers citing it · 8 sentences without a confident label

Compares with it 1 paper

This is exactly what happens also in the IIA case of [ref] , in which the trombone deformation associated to the gauged IIA theory of [ref] is not compatible with the Romans deformation.

The very-extended trombone · D=9 · 0.92

Cites it as background 1 paper

Its gauging was studied for example in [ref] , [ref] .

Supermembrane origin of type II gauged supergravities in 9D · Preliminars · 0.96

What it cites · 58 sentences without a confident label

Builds on 3 papers

In this paper we show that the construction of [ref] admits additional deformations that are associated to the gauging of the trombone symmetry.

Local E(11) · Introduction · 0.99
The main aim of this section is to perform for the gauged IIA theory of [ref] an analysis equivalent to the one performed in [ref] for the Scherk-Schwarz reduction of the IIB theory.

A New Massive Type IIA Supergravity From Compactification · Local $E_11$ and gauged IIA · 0.89
We now want to derive the field strengths and gauge transformations of the gauged IIA theory of [ref] in an analogous way.

Fibre Bundles and Generalised Dimensional Reduction · Local $E_11$ and gauged IIA · 0.85

Uses the method or tool of 2 papers

Applying the same arguments of [ref] , which are reviewed in section 2, we obtain that imposing that the symmetric part in $ab$ of eq.

Local E(11) · Local $E_11$ and gauged IIA · 0.88
This is exactly the method explained in [ref] and applied in [ref] to derive the deformed algebra associated to any gauged maximal supergravity in any dimension.

The E(11) origin of all maximal supergravities - the hierarchy of field-strengths · Local $E_11$ and gauged IIA · 0.98

Compares with 4 papers

This can be seen explicitly by observing that the field strength of the IIA 9-form that one obtains from the deformed $E_11$ algebra associated to the Romans theory [ref] coincides up to field redefinitions with the 9-form that one obtains imposing the closure of the supersymmetry algebra [ref] , which also imposes the duality of its field strength with the Romans mass.

Local E(11) · Conclusions · 0.91
This can be seen explicitly by observing that the field strength of the IIA 9-form that one obtains from the deformed $E_11$ algebra associated to the Romans theory [ref] coincides up to field redefinitions with the 9-form that one obtains imposing the closure of the supersymmetry algebra [ref] , which also imposes the duality of its field strength with the Romans mass.

New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls · Conclusions · 0.91
This can be seen explicitly by observing that the field strength of the IIA 9-form that one obtains from the deformed $E_11$ algebra associated to the Romans theory [ref] coincides up to field redefinitions with the 9-form that one obtains imposing the closure of the supersymmetry algebra [ref] , which also imposes the duality of its field strength with the Romans mass.

IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories · Conclusions · 0.91

Cites as background 5 papers

In this section we first review the formulation of gravity as a non-linear realisation of [ref] , and we then show that deformations of this algebra correspond to field redefinitions, and we finally discuss the issue of frame dependence in the dimensional reduction.

Local E(11) · On gravity as a non-linear realisation · 0.88
Maximal supergravity theories have a very elegant and natural classification in terms of the very-extended infinite-dimensional Kac-Moody algebra $E_11$ [ref] .

E_11 and M Theory · Introduction · 0.96
The symmetry under rescaling of the fields was called “trombone” symmetry in [ref] , because although it is a symmetry of the field equations, it actually gives rise to an overall scaling of the lagrangian.

Fibre Bundles and Generalised Dimensional Reduction · Local $E_11$ and gauged IIA · 0.94

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