Physics Letters B 790 (2019) 415–420
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
κ-deformed BMS symmetry
Andrzej Borowiec
a
, Lennart Brocki
a
, Jerzy Kowalski-Glikman
a,b,∗
, Josua Unger
a
a
Institute for Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204 Wrocław, Poland
b
National Centre for Nuclear Research, Ho ˙za 69, 00-681 Warsaw, Poland
a r t i c l e i n f o a b s t r a c t
Article history:
Received
27 November 2018
Received
in revised form 23 January 2019
Accepted
30 January 2019
Available
online 4 February 2019
Editor:
M. Cveti
ˇ
c
Keywords:
BMS
symmetry
Symmetry
deformations
Hopf
algebras
We present the quantum κ-deformation of BMS symmetry, by generalizing the lightlike κ-Poincaré
Hopf algebra. On the technical level our analysis relies on the fact that the lightlike κ-deformation of
Poincaré algebra is given by a twist and the lightlike deformation of any algebra containing Poincaré as a
subalgebra can be done with the help of the same twisting element. We briefly comment on the physical
relevance of the obtained κ-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.
© 2019 The Authors. 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
.
In the recent years there is a surge of interest in BMS symmetry
at null infinity of asymptotically flat spacetimes [1], [2], [3]. This
renewed interest in the seemingly exotic aspects of classical gen-
eral
relativity was fueled by the discovery of a surprising and close
relationship between asymptotic symmetries and soft gravitons
theorem [4] that, as it turned out, has its roots in Ward identities
for supertranslations [5], [6]. Moreover, the gravitational memory
effect [7] appears to be related to the two [8], so that there is
a triangle of interrelationships, which vertices are BMS symmetry,
Weinberg’s soft graviton theorem, and the memory effect. The ex-
tensive
discussion of these effects can be found in recent reviews
[9] and [10].
It
has also been argued recently [11] that the similarity of null
infinity and black hole horizon suggests that the charges associ-
ated
with the BMS symmetry might be present at the black hole
horizon, so that the black hole might have an infinite number of
hairs, so-called soft hairs, in addition to the three classical one:
mass, charge, and angular momentum. It was argued in [11] and
[12] that the presence of these charges may help solving the black
hole information paradox.
In
this letter we will investigate the properties of a κ-deformed
generalization of the BMS symmetry. There are several reasons to
be interested in such a generalization. The main one is that it
is believed that investigations of κ-deformation might shed some
light on the properties of elusive quantum gravity. The deforma-
tion
parameter of κ-deformation of Poincaré algebra [13–17], see
*
Corresponding author.
E-mail
address: jerzy.kowalski-glikman@ift.uni.wroc.pl (J. Kowalski-Glikman).
[18]for a recent review and more references, has dimension of
mass, and therefore it is natural to identify it with Planck mass, or
inverse Planck length, which in turn suggests a possible close rela-
tionship
between this deformation and quantum gravity. In fact, it
was shown in [19] that in the case of gravity in 2 + 1dimensions
the κ-Poincaré algebra is the algebra of symmetries of quantum
flat space in non-perturbatively quantized quantum gravity, and
therefore it plays in quantum gravity the role analogous to the
fundamental role played by the Poincaré algebra in quantum field
theory.
There
are three incarnations in which κ-deformation can ap-
pear.
First, there is the mostly studied deformation in time direc-
tion,
in which case the rotations subalgebra of the Poincaré algebra
is kept undeformed. This deformation satisfies a natural require-
ment
that rotations are not deformed, and in particular that the
angular momentum and spin composition laws are not modified. It
is for this same reason that space-like κ-deformation with a pre-
ferred
spacial direction of deformation was never considered to be
a phenomenologically viable possibility, and is treated as a mathe-
matical
curiosity with no real relevance for physics.
The
third possibility is the lightlike κ-deformation [20–27]. In
contrast to the previous two cases it is implemented by a trian-
gular
r-matrix, which satisfies the Classical Yang–Baxter Equation.
A remarkable property of this so-called non-standard deformation
is that it is given by a twist which makes its structure much sim-
pler
to construct [28]. Particularly, any embedding of the algebra
into a larger Lie algebra preserves the triangular structure and al-
lows
to perform the deformation by the same twist element. Since
the BMS algebra is ultimately tied in with null infinity and con-
tains
the Poincaré subalgebra, in this paper we deform it using
https://doi.org/10.1016/j.physletb.2019.01.063
0370-2693/
© 2019 The Authors. 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_38721652
- 粉丝: 3
- 资源: 935
我的内容管理
展开
最新资源
- 多传感器数据融合手册：国外原版技术指南
- MyEclipse快捷键大全，提升编程效率
- 从零开始的编程学习：Linux汇编语言入门
- EJB3.0实例教程：从入门到精通
- 深入理解jQuery源码：解析与分析
- MMC-1电机控制ASSP芯片用户手册
- HS1101相对湿度传感器技术规格与应用
- Shell基础入门：权限管理与常用命令详解
- 2003年全国大学生电子设计竞赛：电压控制LC振荡器与宽带放大器
- Android手机用户代理(User Agent)详解与示例
- Java代码规范：提升软件质量和团队协作的关键
- 浙江电信移动业务接入与ISAG接口实战指南
- 电子密码锁设计：安全便捷的新型锁具
- NavTech SDAL格式规范1.7版：车辆导航数据标准
- Surfer8中文入门手册：绘制等高线与克服语言障碍
- 排序算法全解析：冒泡、选择、插入、Shell、快速排序
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
