Triality in minimal model holography
By M. Gaberdiel, Rajesh Gopakumar. 2012
251 citations recorded by the source corpus.
A bstractThe non-linear $ {\mathcal{W}_{\infty }}\left[ \mu \right] $ symmetry algebra underlies the duality between the $ {\mathcal{W}_N} $ minimal model CFTs and the hs[μ] higher spin theory on AdS3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a ‘triality’) between three (generically) distinct values of the parameter μ. This explains, among other things, the agreement of symmetries between the $ {\mathcal{W}_N} $ minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest $ {\mathcal{W}_{\infty }}\left[ \mu \right] $ representations, thereby clarifying the analytic continuation between the ‘light states’ of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/f789975e826837af300b8ab30fb3f5e62c4a5446
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
In Nuclear and High Energy Physics
Citations in the corpus
- Large \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 holography (2013, unknown): “One would also expect that the quantum algebra s ˜ W (4) ∞ [ µ ] should exhibit some sort of triality identifications as in [39] (or as in [40] for N = 2).”
- Bounding the space of holographic CFTs with chaos (2016, methodology): “In [68], the structure of the quantum (i.”
- One loop tests of higher spin AdS/CFT (2013, methodology): “A refinement of the original conjecture of [43] was also presented in [47], with a similar conclusion that the perturbative spectrum of the bulk theory should only include two real scalar fields with the same choice of boundary condition, i.”
- Minimal model holography (2012, background): “Thus, one is led to propose that only the states of the form ( +; 0) should have a perturbative origin in the higher spin theory [58].”
- Higher spins & strings (2014, background): “These, or equivalently, the (Λ; 0) primaries are additional ‘non-perturbative’ states which have some reflection in the Vasiliev theory (albeit in a non-unitary semi-classical limit) [32, 49, 50, 51, 52, 53, 54], but whose precise role has not been completely elucidated.”
- Black holes in three dimensional higher spin gravity: a review (2012, background): “A concrete connection between bulk and boundary is given by a conjectured AdS/CFT duality due to Gaberdiel and Gopakumar [49,50].”