Singletons in supersymmetric field theories and in supergravity

Abstract We consider N = 1 supergravity coupled to a Wess–Zumino multiplet with a potential such that the resulting AdS energies saturate the unitarity and Breitenlohner–Freedman bounds, respectively. Imposing regular boundary conditions that preserve supersymmetry and support finite norms, the spectrum forms an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mi>S</mml:mi> <mml:mi>p</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> supermultiplet in which the singleton representation is absent. We study the case in which this boundary condition is relaxed such that the singleton and its superpartners survive and form an indecomposable representation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mi>S</mml:mi> <mml:mi>p</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> . Focusing on the global limit of the model, we carry out its holographic renormalization, in which a singletonic action makes appearance in the boundary action. Contribution to Stanley Deser memorial volume ‘Gravity, Strings and Beyond’