A unique coupling of the massive spin-2 field to supergravity

A bstract We show that the coupling of a massive spin-2 field to undeformed $$ \mathcal{N}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> supergravity in four dimensions is unique, leading to a specific non-minimal coupling to the Riemann tensor. The massive spin-2 coupling reproduces the one of an oscillator mode in open string theory, while the massive spin-1 coupling includes a higher-derivative term that is expected to violate causality in the background of a gravitational shock wave. We argue that the resolution of causality and the unitarity bound in the Regge limit require the introduction of infinitely many higher-spin fields similar to the Regge trajectories in string theory, therefore providing an argument in favour of the string lamppost principle with minimal supersymmetry in four dimensions. To obtain this result, we construct the general stress-energy tensor multiplet for the massive spin-2 multiplet with $$ \mathcal{N}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> supersymmetry.