Stochastic Quantization and AdS/CFT

Abstract

We argue that there is a relationship between stochastic quantization and AdS/CFT, and we present an explicit calculation to support our claim. In particular, we show that a conformally coupled scalar with phi4 interaction on AdS4 is related, via stochastic quantization as well as via AdS/CFT, to a massless scalar with phi6 interaction in 3d. We show that our results have an underlying geometric origin, which might help to elucidate further the proposed relationship between stochastic quantization and holography.

15 pages; v2: added references

References in corpus (7)

• Quantum Gravity at a Lifshitz Point
• Setting the boundary free in AdS/CFT
• Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
• Relating Field Theories via Stochastic Quantization
• Stochastic quantization and the role of time in quantum gravity
• Instantons and Conformal Holography

Cited by in corpus (13)

• AdS_4/CFT_3 Construction from Collective Fields
• Stochastic quantization and holographic Wilsonian renormalization group
• Stochastic quantization of conformally coupled scalar in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass
• Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion
• Instantons in AdS${}_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT${}_3$'s
• Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• Analytic Continuation of Stochastic Mechanics
• Stochastic Quantization of Relativistic Theories
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation