T-duality constraint on effective Lagrangians

TL;DR

This paper demonstrates how $O(1,1)$ symmetry constrains effective Lagrangians in string theory, explicitly calculating invariant forms at $ ext{α'}$ order and relating them to known actions.

Contribution

It provides explicit calculations showing $O(1,1)$ symmetry enforces constraints on effective Lagrangians and identifies invariant forms corresponding to known string actions.

Findings

$O(1,1)$-invariant Lagrangians are derived at $ ext{α'}$ order.

The invariant Lagrangians match the Metsaev-Tseytlin and Miessner actions.

Residual total derivative terms can be eliminated by symmetry constraints.

Abstract

Recent studies have highlighted the significant role of utilizing $O(1,1)$ symmetry in the circular reduction of effective actions to determine NS-NS couplings in the effective action of string theory. However, these calculations often result in residual terms as total derivatives that do not conform to $O(1,1)$ transformations. In this paper, we present explicit calculations at $\alpha'$ order, demonstrating the enforceability of this symmetry on effective Lagrangians to establish the parameters governing covariant couplings in any scheme. Notably, we discover the $O(1,1)$-invariant Lagrangians corresponding to the Metsaev-Tseytlin action and the Miessner action.