Large-N collective fields and holography
By Sumit R. Das, A. Jevicki. 2003
162 citations recorded by the source corpus.
We propose that the Euclidean bilocal collective field theory of critical large-N vector models provides a complete definition of the proposed dual theory of higher spin fields in anti\char21{}de Sitter spaces. We show how this bilocal field can be decomposed into an infinite number of even spin fields in one more dimension. The collective field has a nontrivial classical solution which leads to an $O(N)$ thermodynamic entropy characteristic of the lower dimensional theory, as required by general considerations of holography. A subtle cancellation of the entropy coming from the bulk fields in one higher dimension with $O(1)$ contributions from the classical solution ensures that the subleading terms in thermodynamic quantities are of the expected form. While the spin components of the collective field transform properly under dilatational, translational, and rotational isometries of AdS, special conformal transformations mix fields of different spins indicating a need for a nonlocal map between the two sets of fields. We discuss the nature of the propagating degrees of freedom through a Hamiltonian form of collective field theory and argue that nonsinglet states which are present in an Euclidean version are related to nontrivial backgrounds.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/04e3e1266140a78184e3786a80093f36994edcf0
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Citations in the corpus
- Bi-local holography in the SYK model (2016, unknown): “This collective representation systematically incorporates arbitrary n-point bi-local correlators and generates the corresponding SD equations in terms of closed set of observables that provide a holographic interpretation [28].”
- d = 3 bosonic vector models coupled to Chern-Simons gauge theories (2011, background): “Perhaps the attempted derivations of the AdS/CFT correspondence for λ = 0 [10, 11, 12, 13] can be generalized to finite λ, by replacing the scalar bilinear operators φi(x)φi(y) appearing in these derivations by a gauge-invariant bilinear (in which the two scalars are connected by an open Wilson line”
- Three dimensional view of the SYK/AdS duality (2017, unknown): “This, therefore, realizes the naive form of the proposal of [50].”
- Partition functions of higher spin black holes and their CFT duals (2011, background): “Relatively recently, it has been realized that higher spin theories may lead to soluble examples of the AdS/CFT correspondence [3,4,5,6,7,8,9,10,11,12,13,14,15,16].”
- The higher spin/vector model duality (2012, background): “Some approaches towards deriving the higher spin/vector model duality from first principles were investigated in [22] and [23–26] (see also [27] for relevant earlier work).”
- Chern–Simons theory with vector fermion matter (2011, background): “See also [51], [52], [53] for applications to holography and higher spin theories.”
- Emergent spacetime and holographic CFTs (2011, unknown): “See [43], [44], [45], [46], [47], [48] for related work.”
- How higher-spin gravity surpasses the spin-two barrier (2010, unknown): “Intermediate developments were given in [130, 131, 132, 133, 134, 135, 136, 137, 138, 139].”
- Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, result): “Strong evidence for this equivalence was found in [14, 15], and suggested derivations of the equivalence were presented in [16, 17, 18, 19].”