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

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.

32 pages, minor changes, references added

References in corpus (15)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Background Field Equations for the Duality Symmetric String
• Frame-like Geometry of Double Field Theory
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• Strings and Branes are Waves
• D-branes in Generalized Geometry and Dirac-Born-Infeld Action
• Cosmological Implications from O(D,D)
• Nambu Sigma Model and Branes
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Extended generalized geometry and a DBI-type effective action for branes ending on branes
• Non-commutativity from the double sigma model
• Dimensional Reduction of the Generalized DBI

Cited by in corpus (6)

• Semi-doubled Sigma Models for Five-branes
• Open string T-duality in double space
• Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories
• Geometric Low-Energy Effective Action in a Doubled Spacetime
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• The invariant action for solitonic 5-branes