New Einstein-Sasaki spaces in five and higher dimensions

Area of Science:

• Differential Geometry
• Mathematical Physics
• String Theory

Background:

• Einstein-Sasaki metrics are crucial in understanding Einstein manifolds and Sasaki-Einstein manifolds, which have applications in string theory and M-theory.
• The study of black hole solutions, particularly rotating ones like Kerr-de Sitter, provides a framework for exploring exotic spacetime geometries.

Purpose of the Study:

• To derive infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds.
• To explore the relationship between black hole metrics and Sasaki-Einstein manifolds through BPS limits.
• To investigate the properties and applications of these new metrics in higher dimensions.

Main Methods:

• Utilizing the BPS (Bogomol'nyi–Prasad–Sommerfield) limit of rotating Kerr-de Sitter black hole metrics.
• Applying Euclideanization to transform the black hole metrics.
• Analyzing the resulting metrics for cohomogeneity and isometry groups.

Main Results:

• Obtained infinite classes of new Einstein-Sasaki metrics on complete, nonsingular manifolds.
• Identified new Einstein-Sasaki spaces L(p,q,r) in five dimensions with cohomogeneity 2 and U(1)xU(1)xU(1) isometry, topologically S(2)xS(3).
• Derived new Einstein-Sasaki spaces in all odd dimensions D = 2n + 1 >= 5 with U(1)(n+1) isometry.

Conclusions:

• The new Einstein-Sasaki spaces provide novel examples for studying geometric structures in theoretical physics.
• The AdS/CFT (Anti-de Sitter/Conformal Field Theory) duals of these spaces describe quiver theories on the 4D boundary of AdS(5), linking geometry to quantum field theory.
• These findings contribute to the ongoing exploration of the interplay between general relativity, string theory, and quantum field theory.