w_{1+∞} Algebra with a Cosmological Constant and the Celestial Sphere

Area of Science:

• Theoretical physics
• Quantum gravity
• String theory

Background:

• Strominger's infinite-dimensional w_{1+∞} algebra describes soft graviton symmetries.
• The role of cosmological constants in symmetry algebras is an active area of research.

Purpose of the Study:

• To investigate a deformed version of the w_{1+∞} algebra.
• To explore its potential emergence in spacetimes with a nonvanishing cosmological constant.
• To analyze the symmetry properties generated by this deformed algebra.

Main Methods:

• Conjectural derivation of a deformed w_{1+∞} algebra.
• Analysis of subalgebraic structures within the deformed algebra.
• Investigation of transformation properties of symmetry currents.

Main Results:

• Existence of a simple deformed w_{1+∞} algebra.
• The deformed algebra contains a subalgebra generating SO(1,4) or SO(2,3) symmetry groups.
• These symmetries correspond to de Sitter (dS_{4}) or anti-de Sitter (AdS_{4}) spacetimes, depending on the cosmological constant's sign.

Conclusions:

• The deformed w_{1+∞} algebra provides a framework for understanding symmetries in spacetimes with cosmological constants.
• This work offers insights into the structure of gauge and gravitational symmetries in curved spacetimes.