| Time：1131206 (Fri.) 10:00~12:00 Speaker：Arpita Mitra Postdoctoral Fellow, Department of Physics, Pohang University of Science and Technology, South Korea Title：Exploring some aspects of Nielsen and Krylov complexity Abstract： In recent years, there has been significant interest in assigning cost for preparing a state within AdS/CFT holography, spurred by Susskind’s conjecture linking the notion of quantum complexity to black hole interior growth. I will discuss a relation between 2 notions of quantum complexity: Nielsen’s approach towards circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating Kähler structures on the full projective Hilbert space of low rank algebras. This geometric structure of the states in the Hilbert space ensures that every unitary transformation of the associated algebras leave the metric and the symplectic forms invariant. We further associate a classical matter free Jackiw-Teitelboim gravity model with these state manifolds and show that the dilaton can be interpreted as the quantum mechanical expectation values of the symmetry generators. On the other hand we identify the dilaton with the spread complexity over a Krylov basis thereby proposing a geometric perspective connecting two different notions of complexity. In the second part of my talk, I will discuss a perturbative correction to the Krylov complexity for two-dimensional conformal field theories under integrable deformations. Specifically, I will consider the consequences of T\bar{T}, J \bar{T}, and J \bar{J} deformations, focusing on first-order corrections in the deformation parameter. Under T\bar{T} deformation, we demonstrate that the Krylov exponent characterizing the rate of exponential growth of complexity surpasses that of the undeformed theory for positive value of deformation parameter, suggesting a potential violation of the conjectured operator growth bound within the realm of perturbative analysis. Place：F101, Gongguan Campus, NTNU |
