Abstract
The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of alpha ' and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order alpha '^2 and for NS–NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.
Highlights
Perturbative string theory is a quantum theory of gravity with a finite number of massless fields and a tower of infinite number of massive fields reflecting the stringy nature of the gravity at the weak coupling
The Double Field Theory and T-duality approaches are based on the observation made by Sen in the context of closed string field theory [15] that the classical effective action of bosonic string theory should be invariant under T-duality to all orders in α
In this paper we have shown that imposing the gauge symmetry on the world-volume couplings of Op-plane in type II superstring theories, one finds at least 48 independent NS– NS couplings with arbitrary coefficients
Summary
Perturbative string theory is a quantum theory of gravity with a finite number of massless fields and a tower of infinite number of massive fields reflecting the stringy nature of the gravity at the weak coupling. The S-duality constraint (5) for D3-brane/O3-plane is such that the combination of world-volume action and its boundary terms should be written in an S-duality invariant form up to some total derivative terms in the world-volume boundary ∂ M(4) which are zero by the Stokes’s theorem. To study the S-duality at order α 2, one needs to take into account R–R fields as well in which we are not interested in this paper It has been observed in [32] that it is impossible to combine couplings in the Einstein frame involving odd number of dilatons and zero B-field with corresponding R–R couplings to be written in an S-duality invariant form. 2.3, we show that the bulk couplings that are fixed by the gauge symmetry and the T-duality, are consistent with S-duality up to some total derivative terms which are transferred to the boundary by using the Stokes’s theorem.
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