Wormholes with scalar fields

Wormholes solutions are discussed in a theory with antisymmetric 3-rank tensor field H_{mu nu rho} (axion) coupled to scalar fields. The authors also consider a generalised gravity theory, which action is given by S= integral d⁴x square root -g(F( phi ,R)-¹/₂h( phi )( Del phi )²-g² H_{mu nu rho}²), with F( phi ,R) and h( phi ) being arbitrary functions of a scalar phi and a scalar curvature R. Since it is conformally equivalent to the Einstein-Hilbert system with H_{mu nu rho} coupled to a scalar field, the authors can apply the above discussion to such a theory. Most models (R² model, Jordan-Brans-Dicke theory, Zee's induced gravity model and the Einstein theory with non-minimal coupling) contain wormhole solutions. Although a wormhole solution cannot occur in the four-dimensional effective theory from a superstring model (Giddings and Strominger (1988)), if the effective theory has a scalar field (not dilaton) coupled non-minimally, a wormhole solution becomes possible.