Abstract
We consider N=4 conformal supergravity with an arbitrary holomorphic function of the complex scalar S which parametrizes the SU(1,1)/U(1) coset. Assuming non-vanishings vevs for S and the scalars in a symmetric matrix Eij of the 10¯ of SU(4) R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that S-supersymmetry is always broken whereas Q-supersymmetry exists only on flat Minkowski spacetime.
Highlights
Conformal supergravity is the supersymmetric completion of conformal or Weyl gravity, described by the Weyl square term
It is invariant under the full superconformal group, which is the supergroup SU (2, 2|N ), the real form of SL(4|N ), where N counts the number of supersymmetries
We have studied possible vacua of maximal N = 4 conformal supergravity which is the supersymmetric completion of conformal or Weyl gravity
Summary
Conformal supergravity is the supersymmetric completion of conformal or Weyl gravity, described by the Weyl square term It is invariant under the full superconformal group, which is the supergroup SU (2, 2|N ), the real form of SL(4|N ), where N counts the number of supersymmetries. Conformal supergravity can be obtained as the massless limit m → 0 of the supersymmetric completion of m2 R + Weyl 2 gravity [16,17,18] (see [19,20,21,22]) Such theories contain ghost propagating states [23,24,25], they are interesting as they arise in the twistor-string theory via closed strings or gauge singlet open strings [26].
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