Complexity, AdS/CFT, and Matrix Models.

• Grant number: 24/13362-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2024
• End date: May 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Horatiu Stefan Nastase
• Grantee: Eric Lobato Graef
• Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
• Associated research grant: 19/21281-4 - Gauge / gravity duality, AP.TEM

Abstract

Quantum complexity is a recently introduced concept, describing a relation of a quantum state to a reference state, and in the context of Quantum Field Theory (QFT), it was first defined in AdS/CFT. More recently, in 2019, Krylov complexity (and later spread complexity) was introduced, as an algorithmically calculated quantity, also related to a notion of entropy, and capable of detecting chaotic behaviour. We will use a toy model, a simplification of the simplest (gravity dual) quantum mechanical model of a black hole, specifically a black hole in AdS2, to test whether Krylov complexity detects the chaotic behaviour. Next, we will consider the Penrose limit ofthe duality between Nielsen complexity of a QFT and a volume in the gravity dual, as well as Krylov complexity and its possible gravity dual. Finally, we consider deformations of the black hole in AdS2 solution: we will write the solutions, and investigate the corresponding Matrix Model deformations.