Exactly Marginal Deformations and Their Supergravity Duals

Area of Science:

• Theoretical physics
• String theory
• Supersymmetry

Background:

• Investigating Anti-de Sitter (AdS) spaces and their dual Conformal Field Theories (CFTs) is crucial for understanding quantum gravity.
• Supersymmetric solutions in type IIB supergravity are key to exploring these dualities.
• The conformal manifold of N=1 conformal field theories describes their possible deformations.

Purpose of the Study:

• To find the gravity duals of generic N=1 deformations of N=4 conformal field theory.
• To establish a proof-of-existence for these supergravity solutions.
• To derive new results for the Hilbert series of these deformed field theories.

Main Methods:

• Studying the space of supersymmetric AdS_{5} solutions in type IIB supergravity.
• Identifying a generalized holomorphic structure within the background geometry.
• Employing a continuity argument to demonstrate the existence of the full solution.

Main Results:

• The background geometry of these solutions naturally encodes a generalized holomorphic structure.
• This structure is dual to the superpotential of the field theory.
• A proof-of-existence for the supergravity solution of generic N=1 deformations of N=4 conformal field theory is provided.
• A new result for the Hilbert series of the deformed field theories is derived.

Conclusions:

• The generalized holomorphic structure provides a framework for understanding the dual field theories.
• This work offers a significant step towards explicitly constructing gravity duals for N=1 supersymmetric field theories.
• The derived Hilbert series results offer new insights into the properties of these deformed theories.