AdS/CFT and the Little Hierarchy Problem

Abstract

The AdS/CFT correspondence is applied to a close analogue of the little hierarchy problem in $AdS_{d+1}$, $d \geq 3$. The new mechanism requires a Maxwell field that gauges a $U(1)_R$ symmetry in a bulk supergravity theory with a negative cosmological constant. Supersymmetry is explicitly broken by a non-local boundary term with dimensionless coupling $h$. Non-locality appears to cause no pathology, and the SUSY breaking deformation engendered is exactly marginal. SUSY breaking effects in the bulk are computed using the $U(1)$ Ward identity. Conformal dimensions and thus masses of scalar and spinor partners are split simply because they carry different R-charges. However SUSY breaking effects cancel to all orders for R-neutral fields, even in diagrams with internal R-charged loops. SUSY breaking corrections can be summed to all orders in $h$. Diagrams involving graviton loops do not introduce any further SUSY breaking corrections. A possible scenario for a flat spacetime limit is outlined.