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Krylov Complexity and c-function along RG Flows

2026/08/03 by Carlos Nunez, Dibakar Roychowdhury
Physics and Astronomy · #hep-th

paper · pdf

20 pages, various figures

arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We investigate Krylov spread complexity along holographic renormalisation-group flows using the proposal that its growth rate is captured by the proper radial momentum of an in-falling massive probe. We focus on the second time derivative of the complexity U, which is determined locally by the redshift and radial metric functions of the dual geometry. For Lorentz-invariant domain-wall flows preserving the spacetime dimension, we derive a new relation between U and the covariant central charge ccov. The decrease of the covariant central function towards the infrared is accompanied by a monotonic increase of the complexity acceleration. For the top-down Dp-brane family, we obtain a universal relation. We then examine flows across dimensions, including a twisted compactification from four to two dimensions and from six to four dimensions. In these examples c\rm cov and U are co-monotonic, in sharp contrast with the inverse correlation characteristic of fixed-dimensional flows. We argue that this reversal reflects the reorganisation, rather than simple depletion, of degrees of freedom into lower-dimensional sectors under compactification. Our results identify complexity acceleration as a sensitive geometric diagnostic connecting information spreading, holographic central functions and RG evolution.

Citations