Construction of all N=4 conformal supergravities

Abstract

All N = 4 conformal supergravities in four space-time dimensions are constructed. These are the only N = 4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1, 1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU (1, 1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for non-conformal theories.

Unraveling conformal gravity amplitudes

“…Recently Tseytlin considered general non-minimal N = 4 conformal supergravities, and concluded that they are free of conformal anomalies given that four vector multiplets are added to the spectrum [123]; thus agreeing with the analysis of the minimal theory [124][125][126]. A complete bosonic action for all N = 4 non-minimal conformal supergravity theories -parametrized by a free function -has been proposed by Butter, Ciceri, de Wit and Sahoo [127]. We confirm in this work, by direct calculation of amplitudes from both the double copy and the action, that the Lagrangian of the Berkovits-Witten theory is given by a simple choice of the free function.…”

“…In particular, we have identified a non-minimal N = 4 conformal supergravity Lagrangian whose physical planewave amplitudes are those of the Berkovits-Witten theory [12]. This theory turns out to be a simple case of the infinite class of non-minimal Lagrangians derived by Butter, de Wit, Ciceri and Sahoo [127]. The tree amplitudes are predicted by a double copy between N = 4 super-Yang-Mills and a (DF ) 2 theory, where the latter gauge theory was introduced by Nohle and one of the present authors in ref.…”

“…We now proceed to the Lagrangian description of non-minimal conformal supergravities, and their associated scattering amplitudes. The bosonic parts of the complete class of N = 4 supersymmetric Lagrangians were recently constructed by Butter, Ciceri, de Wit and Sahoo [127]. The SU(4)-singlet part of their Lagrangian is…”

“…In this case, rather than construct an ansatz, we obtained the above Lagrangian directly from ref. [127] by eliminating additional gauge fields associated with conformal symmetries -for details, see appendix B.2. The scalar function F is of primary interest to us, F = 1 corresponding to the already-discussed minimal theory for which all planewave tree-level amplitudes vanish (for m = 0).…”

Conformal geometry and (super)conformal higher-spin gauge theories

“…The conformal superspace approach is at the heart of the construction of all N = 4 conformal supergravity theories in four dimensions[103].…”