Surface terms in effective action of O-plane at order $\alpha'^2$

TL;DR

This paper derives the effective action of O-planes at order α'^2 in type II superstring theories, including boundary terms, using gauge and duality invariance constraints, revealing fixed bulk and boundary structures with independent multiplets.

Contribution

It provides the first derivation of the O-plane effective action at order α'^2, including boundary terms, constrained by gauge invariance and string dualities.

Findings

Bulk and boundary actions are fixed up to one overall factor.

Three multiplets in the boundary action have coefficients independent of bulk couplings.

The approach constrains effective actions using symmetry principles.

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.