N=1 supersymmetric higher spin holography on AdS_3

TL;DR

This work proposes an ${\cal N}=1$ supersymmetric higher spin holography on AdS3 by formulating an ${\cal N}=1$ truncation of the Prokushkin–Vasiliev theory and identifying its dual as the large-N limit of the ${\cal N}=(1,1)$ SO-coset $\frac{\widehat{so}(2N+1)_k \oplus \widehat{so}(2N)_1}{\widehat{so}(2N)_{k+1}}$. The authors verify the duality by matching one-loop bulk partition functions with the CFT partition functions in the 't Hooft limit and by detailing the coset symmetry, including explicit fields with dimensions ${3}/{2}$, 2, 2, and ${5}/{2}$. They develop both bosonic and supersymmetric partitions using branching functions, free-fermion and free-boson techniques, and invariant theory to show how the spectrum and symmetry align between bulk and boundary. The results provide concrete evidence for AdS3/CFT2 in the supersymmetric higher spin regime and lay groundwork for further checks via correlators, RG flows, and Hamiltonian reductions.

Abstract

We propose a duality between a higher spin N=1 supergravity on AdS_3 and a large N limit of a family of N=(1,1) superconformal field theories. The gravity theory is an N=1 truncation of the N=2 supergravity found by Prokushkin and Vasiliev, and the dual conformal field theory is defined by a supersymmetric coset model. We check this conjecture by comparing one loop partition functions and find agreement. Moreover, we study the symmetry of the dual coset model and in particular compute fields of the coset algebra of dimension 3/2, 2, 2 and 5/2 explicitely.

Figures (1)

• Figure 1: A Young tableau Tab$_\Lambda$ of a shape $\Lambda$. In each box of the Young diagram $\Lambda$, we assign a non-negative number $c_{i,j}$ with a rule that $c_{i,j} \leq c_{i,j+1}$ and $c_{i,j} < c_{i+1,j}$. A Young supertableau STab$_\Lambda$ of a shape $\Lambda$ are also given by a Young diagram $\Lambda$ and a non-negative number $c_{i,j}$ in a each box. However, the rules for $c_{i,j}$ are a bit different. The numbers should always satisfy the conditions $c_{i,j} \leq c_{i,j+1}$ and $c_{i,j} \leq c_{i+1,j}$. Further $c_{i,j} < c_{i,j+1}$ if $c_{i,j}$ and $c_{i,j+1}$ are odd, and $c_{i,j} < c_{i+1,j}$ if $c_{i,j}$ and $c_{i+1,j}$ are even.