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

Tomasz R Taylor1,2, Bin Zhu3

  • 1Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.

Physical Review Letters
|June 15, 2024
PubMed
Summary

A deformed w_{1+∞} algebra of soft graviton symmetries is shown to exist in spacetimes with a nonvanishing cosmological constant. This algebra generates SO(1,4) or SO(2,3) symmetry groups for de Sitter or anti-de Sitter spacetimes.

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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.