Large-Ncollective fields and holography

Abstract

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 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 a 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.

Horizon as critical phenomenon

“…For other holographic approaches to the vector models and related conjectures see refs. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. We write the partition function as…”

“…In the vector model, the single-trace operators are the bi-local operators, (φ * i · φ j ) [33,34,39]. In t (0) , one might try to remove the quartic double-trace operator by introducing an auxiliary field,…”

AdS4/CFT3construction from collective fields

“…For other relevant work, see [12][13][14][15]. The relevance of collective fields for higher-spin holography was discussed by Das and one of the present authors [16]. The framework of covariant bi-local collective fields was employed and it was shown that they decompose into an infinite sequence of integer spin fields in one extra dimension.…”

Holography as a gauge phenomenon in Higher Spin duality

“…Here one has an effective re(summation) of Feynman diagrams into effective interaction vertices ( with extra dimensions). As such the approach gives a systematic scheme for construction of the dual AdS theory and provides considerable insight into the origin of holography [17].…”

“…As emphasized in [17] this represents a bulk description of Higher Spin theory. The emergent AdS space-time can be most clearly identified in the light-cone gauge [18].…”