Holography in de Sitter Space via Chern-Simons Gauge Theory

Area of Science:

• Theoretical Physics
• String Theory
• Quantum Gravity

Background:

• Holographic duality principles connect gravitational theories with quantum field theories.
• De Sitter space is a key model in cosmology and quantum gravity research.
• Chern-Simons theories and Wess-Zumino-Witten models are important in 2D conformal field theory.

Purpose of the Study:

• To propose and investigate a holographic duality for classical gravity in three-dimensional de Sitter space.
• To identify the specific conformal field theory (CFT) dual to this gravitational system.
• To explore extensions of this duality to higher spin gravity.

Main Methods:

• Analyzing the partition function of Einstein gravity on Euclidean de Sitter space (S³).
• Comparing it with the partition function of SU(2) Chern-Simons gauge theories in a specific limit (k → -2).
• Utilizing established holographic principles for coset conformal field theories.

Main Results:

• Demonstrated that SU(2) Chern-Simons gauge theories reproduce the Einstein gravity partition function on S³ as k → -2.
• Identified the SU(2) Wess-Zumino-Witten model as the CFT dual to de Sitter gravity at leading semiclassical order.
• Provided supporting evidence through known holography for coset CFTs.
• Presented a higher spin gravity generalization of the proposed duality.

Conclusions:

• Established a novel holographic duality for three-dimensional de Sitter gravity.
• The dual conformal field theory is an SU(2) Wess-Zumino-Witten model in the large central charge limit.
• The findings offer new insights into the relationship between gravity and quantum field theory in de Sitter spacetimes.