RECORD
AdS/CFT Dualities and the Unitary Representations of Non-compact Groups and Supergroups: Wigner versus Dirac
High Energy Physics - Theory · Submitted 18 May 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim I show, in particular, how one can go from the manifestly unitary compact basis of the lowest weight (positive energy) representations of the conformal group (Wigner picture) to the manifestly covariant coherent state basis (Dirac picture).
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
I review the relationship between AdS/CFT (anti-de Sitter / conformal field theory) dualities and the general theory of positive energy unitary representations of non-compact space-time groups and supergroups. I show, in particular, how one can go from the manifestly unitary compact basis of the lowest weight (positive energy) representations of the conformal group (Wigner picture) to the manifestly covariant coherent state basis (Dirac picture). The coherent states labelled by the space-time coordinates correspond to covariant fields with a definite conformal dimension. These results extend to higher dimensional Minkowskian spacetimes as well as generalized spacetimes defined by Jordan algebras and Jordan triple systems. The second part of my talk discusses the extension of the above results to conformal supergroups of Minkowskian superspaces as well as of generalized superspaces defined by Jordan superalgebras. The (super)-oscillator construction of generalized (super)-conformal groups can be given a dynamical realization in terms of generalized (super)-twistor fields.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | I review the relationship between AdS/CFT (anti-de Sitter / conformal field theory) dualities and the general theory of positive energy unitary representations of non-compact space-time groups and supergroups. | contribution 0.54 | 0.46 | 0.12 | asserted 0.69 |
| s1 | I show, in particular, how one can go from the manifestly unitary compact basis of the lowest weight (positive energy) representations of the conformal group (Wigner picture) to the manifestly covariant coherent state basis (Dirac picture). | contribution 0.66 | 0.90 | 0.36 | asserted 1.00 |
| s2 | The coherent states labelled by the space-time coordinates correspond to covariant fields with a definite conformal dimension. | result 0.74 | 0.71 | 0.14 | asserted 1.00 |
| s3 | These results extend to higher dimensional Minkowskian spacetimes as well as generalized spacetimes defined by Jordan algebras and Jordan triple systems. | result 0.85 | 0.68 | 0.11 | asserted 1.00 |
| s4 | The second part of my talk discusses the extension of the above results to conformal supergroups of Minkowskian superspaces as well as of generalized superspaces defined by Jordan superalgebras. | contribution 0.88 | 0.53 | 0.08 | asserted 0.90 |
| s5 | The (super)-oscillator construction of generalized (super)-conformal groups can be given a dynamical realization in terms of generalized (super)-twistor fields. | result 0.53 | 0.50 | 0.11 | asserted 0.66 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
I review the relationship between AdS/CFT (anti-de Sitter / conformal field theory) dualities and the general theory of positive energy unitary representations of non-compact space-time groups and supergroups. I show, in particular, how one can go from the manifestly unitary compact basis of the lowest weight (positive energy) representations of the conformal group (Wigner picture) to the manifestly covariant coherent state basis (Dirac picture). The coherent states labelled by the space-time coordinates correspond to covariant fields with a definite conformal dimension. These results extend to higher dimensional Minkowskian spacetimes as well as generalized spacetimes defined by Jordan algebras and Jordan triple systems. The second part of my talk discusses the extension of the above results to conformal supergroups of Minkowskian superspaces as well as of generalized superspaces defined by Jordan superalgebras. The (super)-oscillator construction of generalized (super)-conformal groups can be given a dynamical realization in terms of generalized (super)-twistor fields.
Human review
References
How the literature uses it
8 arXiv papers cite this in 12 sentences
Papers citing it · 11 sentences without a confident label
Cites it as background 1 paper
-
The generators $(D,M_mn,T_m,K_m)$ are also referred to as generators of the conformal basis, of conformal split of $(2,3)$ [ref] .
On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity · Introduction · 0.94
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.