Background independence of effective actions at critical dimension

Abstract

Recently, by explicit calculations at orders ${\alpha }^{\prime },{\alpha }^{\prime 2},{\alpha }^{\prime 3}$, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, \ie the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order ${\alpha }^{\prime }$ for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.

15 pages, Latex file, no figure. arXiv admin note: substantial text overlap with arXiv:2111.10987; v2: the version appears in PRD

References in corpus (9)

• Frame-like Geometry of Double Field Theory
• Heterotic Effective Action and Duality Symmetries Revisited
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Four-derivative couplings via T-duality constraint
• On NS-NS couplings at order ${\alpha }^{\prime 3}$
• $O(9,9)$ symmetry of NS-NS couplings at order ${\alpha }^{\prime 3}$
• Effective action of string theory at order ${\alpha }^{\prime }$ in the presence of boundary
• $O(25,25)$ symmetry of bosonic string theory at order ${\alpha }^{\prime 2}$
• Surface terms in effective action of O-plane at order ${\alpha }^{\prime 2}$

Cited by in corpus (1)

• T-duality of D-brane versus O-plane actions