002947036 001__ 2947036
002947036 005__ 20251031041858.0
002947036 0248_ $$aoai:cds.cern.ch:2947036$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002947036 035__ $$9arXiv$$aoai:arXiv.org:2510.17975
002947036 037__ $$9arXiv$$aarXiv:2510.17975$$chep-th
002947036 035__ $$9Inspire$$aoai:inspirehep.net:3071688$$d2025-10-30T21:24:14Z$$h2025-10-31T03:00:23Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002947036 037__ $$aCERN-TH-2025-206
002947036 035__ $$9Inspire$$a3071688
002947036 041__ $$aeng
002947036 100__ $$aAmbrosini, Marco$$mmarco.ambrosini@unige.ch$$uU. Geneva (main)$$vDepartment of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1214 Genève 4, Switzerland
002947036 245__ $$9arXiv$$aHolography of K-complexity: Switchbacks and Shockwaves
002947036 269__ $$c2025-10-20
002947036 300__ $$a84 p
002947036 500__ $$9arXiv$$a84 pages including long appendix
002947036 520__ $$9arXiv$$aIn this paper we study Krylov complexity in the presence of single and multiple operators in the DSSYK model, where we can use the analytical techniques coming from chord diagrammatics. One of the results we obtain is that it showcases the switchback effect, when the appropriate ``triple-scaling limit'' is taken, under which the model becomes dual to semiclassical JT gravity. We build on previous work, where it was shown that, in the continuum limit, Krylov complexity is defined as the sum of expectations value of right and left chord number operators. Here we argue that this property signals the emergence of the geometric nature of this notion of K-complexity. We show that in the regime where DSSYK is dual to semi-classical gravity, the light matter chord corresponds to a shockwave insertion in JT gravity. We identify the geodesic-length dual of the operator complexity and extend the relevant holographic dictionary to describe the details of the matter insertions. Additionally, we define a class of two-sided perturbations of the Lanczos algorithm that allows to analyze the switchback effect. In the appropriate semi-classical limit, this perturbed operator complexity is dual to an ERB length in JT gravity with corresponding shockwave insertions. We thus establish that K-complexity exhibits the expected switchback effect and universal late-time linear growth, consistent with previous findings regarding its geometric nature in the holographic bulk-boundary map.
002947036 541__ $$aarXiv$$chepcrawl$$d2025-10-23T04:01:03.458947$$e10845077
002947036 540__ $$3preprint$$aCC BY 4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002947036 595__ $$cCDS
002947036 595__ $$aCERN-TH
002947036 65017 $$2arXiv$$ahep-th
002947036 65017 $$2SzGeCERN$$aParticle Physics - Theory
002947036 690C_ $$aCERN
002947036 690C_ $$aPREPRINT
002947036 700__ $$aRabinovici, Eliezer$$meliezer@mail.huji.ac.il$$uHebrew U.$$uCERN$$vRacah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel$$vCERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland
002947036 700__ $$aSonner, Julian$$mjulian.sonner@unige.ch$$uU. Geneva (main)$$vDepartment of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1214 Genève 4, Switzerland
002947036 8564_ $$82791058$$s4388$$uhttps://cds.cern.ch/record/2947036/files/chord_aL0.png$$y00002 l_{AdS}^2
002947036 8564_ $$82791059$$s1978016$$uhttps://cds.cern.ch/record/2947036/files/2510.17975.pdf$$yFulltext
002947036 8564_ $$82791060$$s28017$$uhttps://cds.cern.ch/record/2947036/files/freezing.png$$y00006 \textbf{On the left:} Intuitive representation of the DSSYK disk with an operator insertion $\mathcal{O}$ (green chord), receiving a two-sided $\Tilde{\mathcal{O}}$ perturbation (red chords) after a time $t_s$. The length is dynamical in the regions shaded in red, where geodesic lengths are anchored to the boundary. Upon the perturbation insertion, the chord length, in the blue-shaded region, freezes to the value it had at time $t_s$, and we have new dynamical variables. \textbf{On the right:} Plot of the perturbed operator complexity $l(t)$ \eqref{eq:perturbed_opcompl_lgt_full}, corresponding to the intuitive representation on the left, with $\Delta=10^{-9}$, $\Delta_m=10^{-7}$ and $2J\lambda t_s=100$. Upon the perturbation insertion in $t_s$, the length freezes to $l_s=l(t_s)$, however, due to the appearance of the two new dynamical variables, it resumes the linear growth after a scrambling time.
002947036 8564_ $$82791061$$s97795$$uhttps://cds.cern.ch/record/2947036/files/OverviewFigure.png$$y00001 Krylov complexity can be understood as the propagation of a wave packet along the Krylov chain, here labeled by the discrete position $n$. In \cite{Ambrosini:2024sre} it was shown that, in a suitable continuum limit, $\lambda\rightarrow 0$, this propagation becomes ballistic, corresponding to the position of a fully localized wave packet whose width goes to zero with $\lambda$, and can be understood as the growth in time of Krylov complexity in the presence of precursor operator insertions. In the so-called triple-scaled limit of DSSYK, which maps to the semiclassical description of JT gravity in an AdS$_2$ bulk, this complexity shows the switchback effect, triggered by the wave packet hitting the critical position $n_s = n(t_s)$ along the, now continuous, Krylov chain which induces the characteristic delay of complexity growth of order of the scrambling time. Indeed, as shown in the complexity profile, $C_K$ lingers around the critical value $C_s$ for a scrambling time. Here we show the case of a single precursor operator, but the picture generalizes to several such insertions.
002947036 8564_ $$82791062$$s28670$$uhttps://cds.cern.ch/record/2947036/files/timefold_example.png$$y00003 A timefold with six operator insertions, denoted by the red dots, between times $t_L$ and $-t_R$: at $t_1$, $t_2$, $t_4$ and $t_6$ we have switchback insertions, while $t_3$ and $t_5$ are through-going.
002947036 8564_ $$82791063$$s13114$$uhttps://cds.cern.ch/record/2947036/files/vertical_m.png$$y00005 8
002947036 8564_ $$82791064$$s17218$$uhttps://cds.cern.ch/record/2947036/files/single_switch.png$$y00004 M
002947036 8564_ $$82791065$$s127501$$uhttps://cds.cern.ch/record/2947036/files/ShockwaveOverview.png$$y00000 Krylov complexity can be understood as the propagation of a wave packet along the Krylov chain, here labeled by the discrete position $n$ and shown in 1a). In \cite{Ambrosini:2024sre} it was shown that, in a suitable continuum limit, $\lambda\rightarrow 0$, this propagation becomes ballistic, corresponding to the position of a fully localised wave packet evolved by a Liouville-like Hamiltonian $H_L \pm H_R$ evolving a general class of states, obtained by perturbing the thermofield double state, (see 1b). The choice of sign corresponds to different bulk dual prescriptions, as we show in Section \ref{sec:bulk_dual}. In all cases, the bulk geometry is that of a shockwave, with energy $E$ inserted above the black hole mass $M$, where the boundary operator dimension is given by $\Delta = E/M$.
002947036 8564_ $$82791066$$s22083$$uhttps://cds.cern.ch/record/2947036/files/timefold_switchop.png$$y00007 4M
002947036 960__ $$a11
002947036 980__ $$aPREPRINT