Supersymmetric truncation of N=3 dilaton Weyl multiplet

TL;DR

The paper investigates how to truncate the four-dimensional $oldsymbol{N=3}$ dilaton Weyl multiplet, which carries $oldsymbol{SU(2) imes U(1) imes U(1)}$ R-symmetry, down to $oldsymbol{N=2}$. It analyzes two inequivalent truncations: one preserving all R-symmetries that yields the known $oldsymbol{N=2}$ vector-dilaton Weyl multiplet and vector multiplet, and another that breaks $oldsymbol{SU(2)}$ to $oldsymbol{U(1)}$, producing a novel $oldsymbol{32+32}$ off-shell $oldsymbol{N=2}$ conformal gravity multiplet with $oldsymbol{U(1)^3}$ local symmetry. Independently, it constructs another $oldsymbol{32+32}$ $oldsymbol{N=2}$ multiplet by coupling the $oldsymbol{N=2}$ scalar-tensor multiplet to the standard Weyl multiplet and breaking $oldsymbol{SU(2)}$ to $oldsymbol{U(1)}$, then proves the two constructions are equivalent via an explicit mapping. Furthermore, this $oldsymbol{32+32}$ multiplet is shown to be gauge-equivalent to a Poincaré supergravity multiplet due to compensator fields, revealing a novel off-shell route to $oldsymbol{N=2}$ Poincaré supergravity. These results illuminate new off-shell structures in $oldsymbol{N=2}$ conformal supergravity and open avenues for exploring truncations of higher $oldsymbol{N}$ dilaton Weyl multiplets.

Abstract

We perform all possible supersymmetric truncations of the four-dimensional N=3 dilaton Weyl multiplet, which realizes an R-symmetry $SU(2) \times U(1) \times U(1)$, to N=2. A particular truncation procedure does not break any of the R-symmetries and leads to the known N=2 vector-dilaton Weyl multiplet and the N=2 vector multiplet. A different truncation procedure breaks the SU(2) part of the R-symmetry to U(1) and leads to a 32+32 off-shell representation of N=2 conformal supergravity with a partially broken R-symmetry. Independently, we construct another 32+32 off-shell multiplet in N=2 conformal supergravity by coupling the N=2 scalar-tensor multiplet to the N=2 standard Weyl multiplet and using the scalar fields present in the scalar-tensor multiplet to break the SU(2) R-symmetry to U(1). We then establish the equivalence between these two multiplets through a mapping. We observe that this 32+32 multiplet is gauge equivalent to a Poincaré supergravity multiplet as it has all the compensators necessary to go from conformal supergravity to Poincaré supergravity.