Carroll versus Galilei from a brane perspective
- PDF / 401,903 Bytes
- 25 Pages / 595.276 x 841.89 pts (A4) Page_size
- 92 Downloads / 192 Views
Springer
Received: April Revised: August Accepted: September Published: October
11, 11, 13, 12,
2020 2020 2020 2020
Carroll versus Galilei from a brane perspective
a
Van Swinderen Institute, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands b Departamento de F´ısica Te´ orica, Universidad de Valladolid, E-47011 Valladolid, Spain c Instituto de F´ısica Te´ orica UAM/CSIC, C/ Nicol´ as Cabrera, 13–15, C.U. Cantoblanco, E-28049 Madrid, Spain
E-mail: [email protected], [email protected], [email protected] Abstract: We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, · · · ). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding p-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincar´e algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background. Keywords: Classical Theories of Gravity, p-branes, Sigma Models ArXiv ePrint: 2003.03062 1
Address after 01-01-20: Van Swinderen Institute, Groningen University.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)066
JHEP10(2020)066
Eric Bergshoeff,a Jos´ e Manuel Izquierdob and Luca Romanoa,c,1
Contents 1
2 Carroll versus Galilei and the Lie algebra expansion
3
3 Examples of Carroll gravity 3.1 3D Carroll gravity 3.2 3D extended Carroll gravity 3.3 4D Carroll gravity 3.4 4D extended Carroll gravity 3.5 Higher order expansion and invariance conditions
5 6 6 7 8 9
4 p-brane sigma models 4.1 Sigma models without central charge symmetry 4.2 Sigma models with a (non-)central charge symmetry
10 10 12
5 Conclusions
19
A Nomenclature
20
B Dimensional reduction
21
1
Introduction
It is well known that the anti-de Sitter algebra allows several contractions to non-relativistic kinematical symmetry algebras [1]. For zero cosmological constant, among these algebras are the Galilei and Carroll algebras. Both algebras can be obtained as a contraction of the Poincar´e algebra which by itself is a contraction of the anti-de Sitter a
Data Loading...
