Explicitly Broken Supersymmetry with Exactly Massless Moduli

TL;DR

This paper presents a solution to the little hierarchy problem in 3D supersymmetry using AdS/CFT, where SUSY is explicitly broken by boundary deformations, yet moduli remain massless due to their R-neutrality.

Contribution

It introduces a boundary deformation in AdS$_3$ supergravity that breaks SUSY explicitly while preserving massless moduli, leveraging the Ward identity for mass shift calculations.

Findings

SUSY breaking is achieved via boundary terms quadratic in gauge fields.

Moduli fields remain massless and R-neutral despite SUSY breaking.

Mass shifts of scalar and spinor fields are calculable to all orders.

Abstract

There is an avatar of the little hierarchy problem of the MSSM in 3-dimensional supersymmetry. We propose a solution to this problem in AdS$_3$ based on the AdS/CFT correspondence. The bulk theory is a supergravity theory in which U(1) $\times$ U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. Since the R-charges of scalar and spinor differ, this generates a SUSY breaking shift of their masses. The Ward identity facilitates the calculation of these mass shifts to any desired order in the strength of the deformation. Moduli fields are massless $R$-neutral bulk scalars with vanishing potential in the undeformed theory. These properties are maintained to all orders in the deformation despite the fact that moduli couple in the bulk to loops of R-charged fields.