ABJ triality: from higher spin fields to strings

By Chi-Ming Chang, Shiraz Minwalla, Tarun Sharma, Xi Yin. 2012

304 citations recorded by the source corpus.

We demonstrate that a supersymmetric and parity violating version of Vasiliev’s higher spin gauge theory in AdS4 admits boundary conditions that preserve N=0,1,2,3,4?> or 6 supersymmetries. In particular, we argue that the Vasiliev theory with U(M) Chan–Paton and N=6?> boundary condition is holographically dual to the 2+1 dimensional U(N)k × U(M)−k ABJ theory in the limit of large N, k and finite M. In this system all bulk higher spin fields transform in the adjoint of the U(M) gauge group, whose bulk t’Hooft coupling is M/N. Analysis of boundary conditions in Vasiliev theory allows us to determine exact relations between the parity breaking phase of Vasiliev theory and the coefficients of two and three point functions in Chern–Simons vector models at large N. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS4×CP3?>, and that the non-Abelian Vasiliev theory at strong bulk ’t Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev’s higher spin particles held together by U(M) gauge interactions. This is illustrated by the thermal partition function of free ABJ theory on a two sphere at large M and N even in the analytically tractable free limit. In this system the traces or strings of the low temperature phase break up into their Vasiliev particulate constituents at a U(M) deconfinement phase transition of order unity. At a higher temperature of order T=NM?> Vasiliev’s higher spin fields themselves break up into more elementary constituents at a U(N) deconfinement temperature, in a process described in the bulk as black hole nucleation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7dacabf8dafe9ea8696f86e4f7ae6e88e14c9711

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The thermal free energy in large N Chern-Simons-matter theories (2012, background): “• It was proposed [1, 2] that these theories (as well as various supersymmetric extensions [3]) have a gravity dual given by a parity breaking version of Vasiliev’s higher-spin theory on AdS4 [9, 10], with a parity-breaking parameter θ that is a function of the ’t Hooft coupling λ (the exact gauge t”
Tensionless strings from worldsheet symmetries (2015, unknown): “see [11] – [14]).”
Baryons, monopoles and dualities in Chern-Simons-matter theories (2015, background): “The generalization of all our discussions to the supersymmetric Chern-Simons-matter theories, whose gravitational duals were discussed in [9], seems to be straightforward, and we will not perform it here.”
Higher spins & strings (2014, methodology): “In the context of the ABJ embedding of higher spin theory on AdS4 [16] one could also view this breaking as coming from the boundary conditions on the bulk fields — this arises as a one loop effect in the bulk Vasiliev theory.”
Correlators of large N fermionic Chern-Simons vector models (2012, methodology): “Analyzing N = 6 theories in these methods would also be interesting, in particular given the relation between Vasiliev’s theory and string theory proposed in [15].”
AdS description of induced higher-spin gauge theory (2013, methodology): “The possibility of imposing modified boundary conditions on spins s ≤ 1 in Vasiliev’s theory was also used in [33] in constructing higher-spin duals of various supersymmetric Chern-Simons matter theories.”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “, in [78, 79, 119].”
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): “We have argued that the corresponding supergravity spectrum can be accounted for in terms of a non-abelian generalisation of the above Vasiliev theory, in close analogy to what was proposed in one dimension higher in [14].”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “This may lead to a more quantitative understanding of the tensionless limit—at least at the level of the free string spectrum—adding to the recent progresses in flat space [249] and in the context of AdS4/CFT3 [250].”
One loop tests of higher spin AdS/CFT (2013, background): “When the ’t Hooft coupling N/k is kept finite, the bulk duals are conjectured [22, 23] to be more general parity breaking Vasiliev’s theories, whose equations of motion contain extra parameters which are mapped to the CFT ’t Hooft coupling.”
Minimal model holography (2012, background): “These would also provide an embedding of the vector-like cosets into a larger string theory, perhaps along the lines of [38].”
The higher spin/vector model duality (2012, methodology): “The dual CFT, which is the N = 3 U(N) Chern-Simons vector model withNf hypermultiplets, is also expected to be dual to a supersymmetric Vasiliev theory with N = 3 boundary condition, described in [14].”
Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal (2015, methodology): “The second definition, inspired by the AdS/CFT correspondence and specific conjectures relating HS theories to certain CFT’s [1, 2, 17, 53, 54], is that HS theories should reproduce the correlation functions of these CFT’s.”