N=1 extension of minimal model holography

TL;DR

This work constructs and analyzes a minimal ${\cal N}=1$ supersymmetric extension of bosonic minimal model holography for AdS3/CFT2, showing there is no free coupling beyond the central charge. The dual bulk theory is the higher spin algebra ${\rm shs}(1|2)$, with the ${\cal N}=1$ ${\cal W}_{\infty}$ algebra as its wedge; the bosonic ${\cal W}_\infty[1/2]$ subalgebra is embedded, and a non-diagonal modular invariant realizes the dual CFT. The spectrum and partition function are matched between the coset CFT and the higher spin theory, requiring an ${\cal N}=1$ matter multiplet in the bulk to account for the full 't Hooft limit. The results establish a concrete example of a non-diagonal ${\cal W}_{\infty}$ invariant with a corresponding higher spin bulk dual, offering a path to exploring similar dualities for other invariants.

Abstract

The CFT dual of the higher spin theory with minimal N = 1 spectrum is determined. Unlike previous examples of minimal model holography, there is no free parameter beyond the central charge, and the CFT can be described in terms of a non-diagonal modular invariant of the bosonic theory at the special value of the 't Hooft parameter lambda=1/2. As evidence in favour of the duality we show that the symmetry algebras as well as the partition functions agree between the two descriptions.