Holography as a gauge phenomenon in Higher Spin duality

Abstract

Employing the world line spinning particle picture. We discuss the appearance of several different 'gauges' which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a 'gauge independent' representation where all gauge constraints are eliminated. This 'gauge reduction' of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3 .

Bi-local holography in the SYK model

“…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]. For the generic case of N -component Vector/Higher Spin Gravity duality [29,30] bi-locality provides an explicit implementation of holography [28,[31][32][33][34][35]. The present SYK system shares analogous features and can be studied along the same line, as the d = 1 case with an AdS 2 dual.…”

ABJ theory in the higher spin limit

“…Meanwhile, the collective field method was applied to the vector models, elucidating how the HS theory can be directly reconstructed from the VM as well as providing a new perspective on the origin of the duality as a gauge phenomenon [21][22][23][24][25][26]. It should also be noted that, pioneered by Gaberdiel and Gopakumar, tremendous progress has been made in the study of the duality between HS theories on AdS 3 and minimal CFT 2 's due to the relative simplicity in lower dimensionality .…”

“…Now, recalling the relation between the Bernoulli polynomial B n (x) and the Bernoulli numbers B n , 25) and also the relation…”

Space-time in the SYK model

“…For all these theories, bi-local observables, as proposed in [76] in the context of O(N ) vector model/higher spin duality [77], provide a route to a bulk construction of the dual theory with emergent space-time [78][79][80]. For the SYK model the IR and the near-IR limit are solvable, with evaluations [2,6,8] of the invariant Schwarzian action representing the boundary Gravity degrees of freedom possibly related to JT type [81,82] dual theory [83][84][85][86][87] (See also [88][89][90][91][92][93][94][95][96][97]).…”

“…We will show that a non-local transform relates the bi-local field to a field whose underlying dynamics is in Euclidean AdS 2 . We will arrive at this transform following the same principles underlying the derivation of the corresponding transform for the O(N ) model in d = 3 [78,79]: the idea is to find a canonical transformation in the four dimensional phase space of the two points in the bi-local such that the symmetries of EAdS 2 are realized correctly. This suggets a simple transformation kernel for the momentum space fields.…”