Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model

TL;DR

This paper explores the boundary conditions and low-energy effective theory of the double sigma model, extending its $O(D,D)$ invariance without strong constraints, and demonstrates classical and quantum equivalence to the normal sigma model.

Contribution

It introduces modified boundary conditions using $O(D,D)$ descriptions, derives the low-energy theory without strong constraints, and constructs a generalized metric ensuring model equivalence.

Findings

The low energy theory maintains $O(D,D)$ invariance.

The one-loop $eta$ function reproduces the normal sigma model.

Different boundary conditions can be constructed via projectors.

Abstract

Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields. We perform the one-loop $\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints. The low energy theory can also be $O(D,D)$ invariant as the double sigma model. We use the other one way to construct different boundary conditions from the projectors. Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric. We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence. We show the one-loop $\beta$ function for the constant background fields and obtain the normal sigma model after integrating out the dual coordinates.