Physics Letters B 779 (2018) 479–484
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
E11 and the non-linear dual graviton
Alexander G. Tumanov
a
, Peter West
b,∗
a
School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel
b
Department of Mathematics, King’s College, London WC2R 2LS, UK
a r t i c l e i n f o a b s t r a c t
Article history:
Received
21 November 2017
Accepted
9 February 2018
Available
online 21 February 2018
Editor:
N. Lambert
The non-linear dual graviton equation of motion as well as the duality relation between the gravity and
dual gravity fields are found in E theory by carrying out E
11
variations of previously found equations of
motion. As a result the equations of motion in E theory have now been found at the full non-linear level
up to, and including, level three, which contains the dual graviton field. When truncated to contain fields
at levels three and less, and the spacetime is restricted to be the familiar eleven dimensional space time,
the equations are equivalent to those of eleven dimensional supergravity.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
It was conjectured that the non-linear realisation of the semi-
direct
product of E
11
with its vector representation (l
1
), denoted
E
11
⊗
s
l
1
, leads to a theory, called E theory, that contains the
eleven dimensional supergravity theory [1,2]. E theory contains an
infinite number of fields that live on a space time that has an in-
finite
number of coordinates. However, the fields at low levels are
just those of eleven dimensional supergravity, in particular at lev-
els
zero, one and two we find the graviton, three and six form
fields respectively. Furthermore, the lowest level coordinate is that
of our familiar eleven dimensional space time. Following early ef-
forts,
for example reference [3], it has been shown that E theory
leads to essentially unique equations of motion which are second
order in derivatives for the graviton and form fields [4,5]. When
these equations of motion are restricted to contain only the su-
pergravity
fields which live on the usual spacetime they are just
those of eleven dimensional supergravity [3,4]. By taking different
decompositions of E
11
one can find all the maximal supergravity
theories including the gauge supergravities and it is inevitable that
the analogous result for the equations of motion holds in all di-
mensions,
for a review and references therein see [6].
The
equations of motion at the linearised level have been found
in eleven dimensions up to and including level four in the fields
[7]. The field at level three is the dual graviton while at level four
there are three fields. It was shown that the dual graviton field
obeyed an equation that did correctly describe the degrees of free-
dom
of gravity and while one of the fields at level four leads to
*
Corresponding author.
E-mail
address: peter.west540 @gmail .com (P. West).
Romans theory, when dimensional reduced to ten dimensions, one
of the other level four fields was dual of the three form. The de-
grees
of freedom resulting from the full system of equations were
those of eleven dimensional supergravity.
The
dual graviton first appeared in five dimensions in the refer-
ence
[8]. This paper was one of the first to consider the dynamics
of fields which carried mixed symmetry indices and it constructed
the equation of motion of the field φ
ab,c
with the symmetries
φ
ab,c
=−φ
ba,c
in a general dimension. The author noted that in
the massless case, and in five dimensions, the equation of motion
for this field had the same number of on-shell degrees of freedom
as the graviton. In reference [9]the field φ
a
1
...a
D−3
,b
was considered
in D dimensions and suggested as a candidate for the dual gravi-
ton
in the sense that a quantity which contained two space–time
derivatives acting on this field could be regarded as being dual to
the Riemann tensor. By assuming the existence of an appropriate
light cone formulation, which would suitable restrict the indices
on the irreducible component of this field to take only D − 2val-
ues,
it was realised that it had the correct number of degrees of
freedom to describe gravity as the [a
1
...a
D−3
] would be equiva-
lent
to a single index.
As
we have mentioned the field that occurs in the E
11
⊗
s
l
1
non-linear realisation at level three in eleven dimensions has the
indices h
a
1
...a
8
,b
and it was proposed that this would satisfy a
duality relation with the usual gravity field that was first order
in derivatives, generalising the duality between the three and six
form fields found at levels one and two respectively [1]. Indeed
an explicit equation of this type, generalised to D dimensions, and
using the field h
a
1
...a
D−3
,b
was given. It was shown that one could
take a derivative of this duality relation so as to obtain an equa-
tion
for the gravity field or the dual gravity field [1]. As a result it
https://doi.org/10.1016/j.physletb.2018.02.015
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
下载后可阅读完整内容，剩余5页未读，立即下载
weixin_38557980
- 粉丝: 7
- 资源: 925
我的内容管理
展开
最新资源
- Unity UGUI性能优化实战：UGUI_BatchDemo示例
- Java实现小游戏飞翔的小鸟教程分享
- Ant Design 4.16.8：企业级React组件库的最新更新
- Windows下MongoDB的安装教程与步骤
- 婚庆公司响应式网站模板源码下载
- 高端旅行推荐：官网模板及移动响应式网页设计
- Java基础教程：类与接口的实现与应用
- 高级版照片排版软件功能介绍与操作指南
- 精品黑色插画设计师作品展示网页模板
- 蓝色互联网科技企业Bootstrap网站模板下载
- MQTTFX 1.7.1版：Windows平台最强Mqtt客户端体验
- 黑色摄影主题响应式网站模板设计案例
- 扁平化风格商业旅游网站模板设计
- 绿色留学H5模板：科研教育机构官网解决方案
- Linux环境下EMQX安装全流程指导
- 可爱卡通儿童APP官网模板_复古绿色动画设计
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
