Supersymmetric 3D anti-de Sitter space solutions of type IIB supergravity

Area of Science:

• Theoretical Physics
• String Theory
• Supersymmetry

Background:

• Kähler-Einstein manifolds are central to geometry and physics.
• Supersymmetric solutions in supergravity theories are key to understanding quantum gravity.
• The anti-de Sitter/conformal field theory (AdS/CFT) correspondence provides a powerful duality between gravity and quantum field theory.

Purpose of the Study:

• To construct new infinite families of supersymmetric solutions in type IIB supergravity.
• To explore the dual conformal field theories (CFTs) associated with these solutions.
• To investigate the properties of these dual CFTs, specifically their supersymmetry and central charges.

Main Methods:

• Construction of supersymmetric solutions using geometric properties of positively curved Kähler-Einstein manifolds.
• Application of the AdS/CFT correspondence to establish duality between the constructed supergravity solutions and 2D CFTs.
• Analysis of the resulting 2D CFTs for their supersymmetry and calculation of their central charges.

Main Results:

• An infinite family of supersymmetric solutions in four-dimensional type IIB supergravity was constructed.
• These solutions are characterized as warped products of anti-de Sitter space in three dimensions (AdS3) with a compact seven-dimensional manifold, featuring nonvanishing five-form flux.
• The solutions are dual, via AdS/CFT, to two-dimensional conformal field theories possessing (0,2) supersymmetry.
• The central charges of these dual 2D CFTs were found to be rational numbers.

Conclusions:

• The study provides a concrete construction of infinite supersymmetric solutions in type IIB supergravity.
• It demonstrates a new class of dualities between higher-dimensional supergravity and lower-dimensional CFTs.
• The findings offer insights into the relationship between geometry, supersymmetry, and quantum field theory through the AdS/CFT correspondence.