Dilaton and axion as compensators coupled toN=1supergravity

Abstract

We present a locally $N=1$ supersymmetric model of the dilaton $\ensuremath{\varphi}$ and the two-form tensor (axion) ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$ as compensators without propagation. This is a generalization of our previous model with global $N=1$ supersymmetry to local $N=1$ supersymmetry. The dilaton $\ensuremath{\varphi}$ and the axion ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$ are, respectively, absorbed into the vector ${A}_{\ensuremath{\mu}}$ and the three-form tensor ${C}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$, where the latter is dual to the ordinary auxiliary field $D$ in the usual vector multiplet. With local $N=1$ supersymmetry, we have three multiplets: the multiplet of supergravity $(e_{\ensuremath{\mu}}{}^{m},{\ensuremath{\psi}}_{\ensuremath{\mu}})$, linear multiplet $({B}_{\ensuremath{\mu}\ensuremath{\nu}},\ensuremath{\chi},\ensuremath{\varphi})$, and the vector multiplet $({A}_{\ensuremath{\mu}},\ensuremath{\lambda},{C}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}})$. We find that the field strengths of $B$ and $C$ need the following particular Chern-Simons terms for consistency with local supersymmetry: $\mathcal{G}\ensuremath{\equiv}3dB\ensuremath{-}6B\mathcal{D}\ensuremath{\varphi}+3mBA+mC$ and $\mathcal{H}=4dC\ensuremath{-}6BF+4\mathcal{G}A+8C\mathcal{D}\ensuremath{\varphi}\ensuremath{-}4mCA$. The newly established supergravity couplings provide the supporting evidence of the consistency of our basic system of the dilaton and axion as compensators.