Non-linear sigma models with anti-de Sitter target spaces

Abstract We present evidence that there is a non-trivial fixed point for the AdS D + 1 non-linear sigma model in two dimensions, without any matter fields or additional couplings beyond the standard quadratic action subject to a quadratic constraint. A zero of the beta function, both in the bosonic and supersymmetric cases, appears to arise from competition between one-loop and higher loop effects. A string vacuum based on such a fixed point would have string scale curvature. The evidence presented is based on fixed-order calculations carried to four loops (corresponding to O ( α ′ 3 ) in the spacetime effective action) and on large D calculations carried to O ( D −2 ) (but to all orders in α ′ ). We discuss ways in which the evidence might be misleading, and we discuss some features of the putative fixed point, including the central charge and an operator of negative dimension. We speculate that an approximately AdS 5 version of this construction may provide a holographic dual for pure Yang–Mills theory, and that quotients of an AdS 3 version might stand in for Calabi–Yau manifolds in compactifications to four dimensions.