Geometric action for nongeometric fluxes.

Area of Science:

• Theoretical Physics
• String Theory
• Mathematical Physics

Background:

• Nongeometric fluxes (Q and R) in string theory lack a clear geometric interpretation.
• Double Field Theory (DFT) offers a framework to unify geometric and nongeometric aspects.

Purpose of the Study:

• To provide a geometric interpretation of the nongeometric Q and R fluxes.
• To reformulate Double Field Theory (DFT) using T-duality inversion.
• To derive a higher-dimensional action incorporating these fluxes.

Main Methods:

• Considered a novel formulation of Double Field Theory (DFT) via T-duality inversion.
• Interpreted the R flux as a tensor under diffeomorphisms with a nontrivial Bianchi identity.
• Viewed the Q flux as part of a connection that covariantizes winding derivatives.

Main Results:

• Established a geometric interpretation for Q and R fluxes within DFT.
• Developed a T-duality inverted formulation of DFT.
• Proposed a higher-dimensional action with kinetic terms for R flux and a dual Einstein-Hilbert term for Q flux.

Conclusions:

• The geometric interpretation clarifies the nature of nongeometric fluxes in string theory.
• The derived action provides a new perspective on higher-dimensional gravity and flux compactifications.
• This work bridges geometric and nongeometric descriptions in theoretical physics.