# Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry

## TL;DR

This paper studies how marginal deformations in a 3d supersymmetric U(N) model affect higher spin symmetries, showing they break these symmetries and give mass to higher spin fields, with dual interpretations in 4d Vasiliev theory.

## Contribution

It computes anomalous dimensions of higher spin currents under marginal deformations in a 3d supersymmetric model to all orders in deformation parameters.

## Key findings

- Higher spin gauge symmetry is broken by marginal deformations.
- Masses are generated for higher spin fields due to symmetry breaking.
- Boundary and bulk computations are related through conformal perturbation theory.

## Abstract

We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.