Mokhtar Hassaine talks with
ScienceWatch.com and answers a few questions about
this month's Fast Breaking Paper Paper in the field of
Article Title: The geometry of Schrodinger symmetry in
Authors: Duval, C;Hassaine, M;Horvathy,
Journal: ANN PHYS N Y, Volume: 324, Issue: 5, Page: 1158-1167,
Year: MAY 2009
* Univ Tours, Lab Math & Phys, Parc Grandmont, F-37200
* Univ Tours, Lab Math & Phys, F-37200 Tours, France.
* CNRS, Ctr Phys Theor, F-13288 Marseille 9, France.
* Univ Talca, Inst Matemat & Fis, Talca, Chile.
Why do you think your paper is highly cited?
Does it describe a new discovery, methodology, or synthesis of
During the past two years, several promising attempts to extend the
anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence to
conformal non-relativistic physics have attracted much attention. This is
motivated by the fact that several non-relativistic conformal field models
that govern physics exist in different experimentally accessible areas,
such as condensed matter physics, atomic physics, or nuclear physics.
I would say that our paper presents another point of view, based entirely
on geometric considerations.
Would you summarize the significance of your paper
in layman's terms?
"At some time in the future, it will be of interest to
investigate the condensed matter interpretation of these
In this AdS/CFT correspondence, one of the main ingredients is that the
isometries of the AdS act on the boundary like the conformal group. The
extension of this correspondence in the non-relativistic case forces us to
find the equivalent of the AdS metric, and that was done by Dam Thanh Son
of the Institute for Nuclear Theory at the University of Washington in his
article: "Toward an AdS/cold atoms correspondence: A geometric realization
of the Schrödinger symmetry," Phys. Rev. D 78: 046003, 2008,
and also by Koushik Balasubramanian and John McGreevy of the MIT Center for
Theoretical Physics in their article: "Gravity Duals for Nonrelativistic
Conformal Field Theories," Phys. Rev. Lett. 101: 061601, 2008.
In our paper, we proposed a geometric approach to explain and derive the
corresponding metric using previous ideas put forward by one of
How did you become involved in this research, and
were there any problems along the way?
We (Christian Duval, Mokhtar Hassaine, and Peter A. Horváthy) were
involved in work on non-relativistic symmetries over a long period of time,
starting with "Bargmann Structures And Newton-Cartan Theory," by C. Duval,
G. Burdet, H.P. Kunzle, M. Perrin, Phys. Rev. D 31:1841,1985 and
"Celestial mechanics, conformal structures and gravitational waves," by C.
Duval, Gary W. Gibbons, and P. Horváthy,
Phys. Rev. D 43:3907-22,1991.
Where do you see your research leading in
There have been new extensions of this non-relativistic version of the
AdS/CFT correspondence for which the Schrödinger group has been
replaced by the Lifshitz group. This new version is more appropriate in the
context of standard holography.
There have been some interesting results in this set-up, with the discovery
of various black hole configurations—see: E. Ayón-Beato, A.
Garbarz, G. Giribet and M. Hassaine, "Lifshitz black hole in three
dimensions," Phys. Rev. D 80: 104029, 2009. At some time in the
future, it will be of interest to investigate the condensed matter
interpretation of these black-hole backgrounds.
Do you foresee any social or political
implications for your research?
We do not have any such intentions. We do research in theoretical physics,
and that's all.
Mokhtar Hassaine, Ph.D.
Instituto de Matematica y Fisica
Universidad de Talca
KEYWORDS: KINEMATICAL INVARIANCE GROUP; MASSIVE GAUGE-THEORIES;
CHERN-SIMONS; CONFORMAL SYMMETRY; FLUID-DYNAMICS; LUMINOUS ETHER; WAVES;
QUANTIZATION; MECHANICS; ELECTRONS.