On the compactification of 5d theories to 4d
Mario Martone, Gabi Zafrir
Abstract
A bstract We study general properties of the mapping between 5 d and 4 d superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5 d SCFT reduces to a 4 d one, we identify nearly all $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 5 d SCFT parents of rank-2 4 d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4 d . This can be done by first understanding the mass deformations of the 5 d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 SCFTs and then map them to 4 d . The former task can be easily achieved by exploiting the fact that the 5 d parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4 d moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.