Weyl multiplets of N=2 conformal supergravity in five Dimensions

TL;DR

The authors construct the Weyl multiplets for N=2 conformal supergravity in five dimensions, revealing two distinct 32+32 formulations: the Dilaton Weyl multiplet (containing a dilaton) and the Standard Weyl multiplet (without a dilaton). They develop linearized transformation rules via a current-multiplet analysis and then obtain full non-linear rules by gauging the D=5 superconformal algebra F^2(4), including a modified, field-dependent algebra. A central result is the precise connection between the two multiplets: coupling the Standard Weyl multiplet to an improved vector multiplet and solving the equations of motion yields the Dilaton Weyl multiplet, establishing a concrete map between formulations. The work lays a rigorous foundation for general matter couplings in 5D conformal supergravity and has potential implications for RS/AdS6/CFT5 setups and holographic dualities. A related contemporaneous study (Fujita et al.) corroborates the existence of the two multiplets and their superconformal tensor calculus in five dimensions.

Abstract

We construct the Weyl multiplets of N=2 conformal supergravity in five dimensions. We show that there exist two different versions of the Weyl multiplet, which contain the same gauge fields but differ in the matter field content: the Standard Weyl multiplet and the Dilaton Weyl multiplet. At the linearized level we obtain the transformation rules for the Dilaton Weyl multiplet by coupling it to the multiplet of currents corresponding to an on-shell vector multiplet. We construct the full non-linear transformation rules for both multiplets by gauging the D=5 superconformal algebra F^2(4). We show that the Dilaton Weyl multiplet can also be obtained by solving the equations of motion for an improved vector multiplet coupled to the Standard Weyl multiplet.