T-duality of α′\alpha'-correction to DBI action at all orders of gauge field

By explicit calculations of four-field couplings, we observe that the higher derivative corrections to the DBI action in flat space-time, can be either in a covariant form or in a T-duality invariant form. The two forms are related by a non-covariant field redefinition. Using this observation, we then propose a non-covariant but T-duality invariant action which includes all orders of massless fields and has two extra derivatives with respect to the DBI action.Comment: 16 pages, latex file, no figure; v3:minor modification, it appears in NP

S-duality constraint on higher-derivative couplings

The Riemann curvature correction to the type II supergravity at eight-derivative level in string frame is given as e^{-2\phi}(t_8t_8R^4+\frac{1}{4}\eps_{8}\eps_{8}R^4). For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors $t_{2n}$ from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality.Comment: 23 pages, Latex file, no figure; v3:some typos correcte