Explicitly Broken Supersymmetry with Exactly Massless Moduli

TL;DR

The paper presents a holographic mechanism where explicit SUSY breaking via a boundary Chern-Simons term in AdS3 completely breaks bulk SUSY while preserving exactly massless moduli. Bulk calculations and boundary CFT analyses show charged fields acquire SUSY-breaking mass shifts, whereas moduli remain massless due to the pure-gauge nature of bulk-to-boundary propagators and Ward identities, with all-order resummations following a necklace structure. The deformation is demonstrated to be exactly marginal, with systematic corrections to correlators and bulk couplings derived and shown to respect CFT constraints. These results offer new insights into moduli protection and hierarchy-like issues in low-dimensional holographic models and raise questions about bulk locality and flat-space limits in SUSY-breaking contexts.

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.

Figures (5)

• Figure 1: The relevant diagrams for the leading order mass deformation of a charged scalar field.
• Figure 2: The relevant diagrams for calculating the leading order deformation of the 1-loop self-energy correction. Here we fix the position of $x'$ while moving $x$ around the loop of the charged field.
• Figure 3: Some additional diagrams needed to calculate the order $h$ deformation of the 1-loop self-energy correction for a scalar with R-charge $(q,\tilde{q})$. Diagrams with seagull vertices on external lines are also needed.
• Figure 4: Higher order SUSY breaking corrections to the two-point correlation functions of R-charged particles. The expansion is done for both $h$ and $q$. One first sums the higher order $h$ expansion with a fixed order $q$, as shown on the left. Then one can further sum the contributions on higher order $q$ expansion as shown on the right.
• Figure 5: Diagrams relevant to the exactly marginal property of the deformation.