Spin Duality Research Articles

Canonical formulation of O(N) vector/higher spin correspondence

We discuss the canonical structure of the collective formulation of vector model/higher spin duality in AdS4. This involves a construction of bulk AdS higher spin fields through a time-like bi-local map, with a Hamiltonian and canonical structure which are established to all orders in .

Holography as a gauge phenomenon in Higher Spin duality

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 CFT3.

1/Nand loop corrections in higher spinAdS4/CFT3duality

We consider the question of loop corrections (i.e. $1/N$) in the vector model/higher spin duality following the recent work of Giombi and Klebanov [J. High Energy Phys. 12, 068 (2013)]. The purpose of this paper is to gain further a more precise comparison between the two sides of the duality. For CFTs given by 3d $O(N)$ or $U(N)$ vector models we evaluate the leading and one-loop partition functions in a variety of geometries. Our calculations are performed in the scheme of collective field theory which was seen in earlier studies to represent a bulk description of Vasiliev higher spin theory. The calculations presented provide data for the comparison of small fluctuation determinants giving further evidence for the one-to-one bulk identification between the bilocal and the AdS pictures. They also offer insight into the identification of coupling constants $G$ and $1/N$ of the two descriptions for models based on $O(N)$ symmetry.

Hierarchy of exactly solvable spin-12chains withso(N)1critical points

We construct a hierarchy of exactly solvable spin-1/2 chains with $so{(N)}_{1}$ critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples $N$ transverse field Ising chains such that the resulting theory is critical and described by the $so{(N)}_{1}$ conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary $N$ into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd $N$ our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even $N$ the models can be viewed as longer ranger generalizations of the $XY$ chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.