β Symmetry of Supergravity.

Area of Science:

• String theory
• High-energy physics
• Quantum gravity

Background:

• Kaluza-Klein reductions are used to unify forces and reduce dimensions in string theory.
• Continuous O(d,d) global symmetries arise in these reductions.
• The physical interpretation and implications of these symmetries are not fully understood.

Purpose of the Study:

• To investigate the role of O(d,d) symmetries in D-dimensional string supergravities.
• To identify the nongeometric elements of O(d,d) as a specific symmetry in the parent theory.
• To explicitly derive and verify the transformations associated with this hidden symmetry.

Main Methods:

• Analysis of Kaluza-Klein reductions of D-dimensional string supergravities.
• Identification of nongeometric symmetry actions within the D-dimensional theory.
• Derivation of first-order transformations in α' for the identified symmetry.
• Verification of action invariance and transformation rule closure.

Main Results:

• Continuous O(d,d) global symmetries emerge from Kaluza-Klein reductions.
• The nongeometric aspects of O(d,d) correspond to a hidden bosonic symmetry, termed β symmetry.
• Explicit β transformations to first order in α' were derived.
• Invariance of the action and closure of the transformation rules under β symmetry were confirmed.

Conclusions:

• The β symmetry is a fundamental, hidden bosonic symmetry in D-dimensional string supergravities.
• This symmetry arises from the nongeometric elements of O(d,d) global symmetries.
• The findings provide a deeper understanding of symmetries in string theory and their impact on couplings.