O(d, d)-Symmetry and Ernst Formulation of Einstein–Kalb–Ramond Theory

Abstract

A Ernst-like matrix representation of (3+d)-dimensional Einstein–Kalb–Ramond theory is developed. The analogy with the Einstein and Einstein–Maxwell–Dilaton–Axion theories is discussed. The subsequent reduction to two dimensions is considered. It is shown that, in this case, the theory allows two different Ernst-like d×d-matrix formulations: the real nondualized target space, and the Hermitian dualized nontarget space one. The O(d, d)-symmetry is written in an SL (2,R) matrix-valued form in both cases. The Kramer–Neugebauer transformation, which algebraically maps the nondualized Ernst potential onto the dualized one, is presented.