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1. Dressing bulk fields in AdS3

   https://doi.org/10.1007/JHEP10(2020)189  

   Kabat, Daniel; Lifschytz, Gilad (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract We study a set of CFT operators suitable for reconstructing a charged bulk scalar field ϕ in AdS 3 (dual to an operator $$ \mathcal{O} $$ O of dimension ∆ in the CFT) in the presence of a conserved spin- n current in the CFT. One has to sum a tower of smeared non-primary scalars $$ {\partial}_{+}^m{J}^{(m)} $$ ∂ + m J m , where J ( m ) are primaries with twist ∆ and spin m built from $$ \mathcal{O} $$ O and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order 1/ N this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line. 

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2. Size of bulk fermions in the SYK model

   https://doi.org/10.1007/JHEP10(2020)053  

   Lensky, Yuri D.; Qi, Xiao-Liang; Zhang, Pengfei (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS 2 bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk SL(2; ℝ) generators. 

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3. Operator Learning Using Random Features: A Tool for Scientific Computing

   https://doi.org/10.1137/24M1648703  

   Nelsen, Nicholas H; Stuart, Andrew M (August 2024, SIAM Review)

   Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as apowerful tool to complement traditional scientific computing, which may often be framedin terms of operators mapping between spaces of functions. Building on the classical ran-dom features methodology for scalar regression, this paper introduces the function-valuedrandom features method. This leads to a supervised operator learning architecture thatis practical for nonlinear problems yet is structured enough to facilitate efficient trainingthrough the optimization of a convex, quadratic cost. Due to the quadratic structure, thetrained model is equipped with convergence guarantees and error and complexity bounds,properties that are not readily available for most other operator learning architectures. Atits core, the proposed approach builds a linear combination of random operators. Thisturns out to be a low-rank approximation of an operator-valued kernel ridge regression al-gorithm, and hence the method also has strong connections to Gaussian process regression.The paper designs function-valued random features that are tailored to the structure oftwo nonlinear operator learning benchmark problems arising from parametric partial differ-ential equations. Numerical results demonstrate the scalability, discretization invariance,and transferability of the function-valued random features method. 

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4. Universal Counterdiabatic Driving in Krylov Space

   https://doi.org/10.1103/wbbs-s8fs  

   Morawetz, Stewart; Polkovnikov, Anatoli (October 2025, PRX Quantum)

   Local counterdiabatic (CD) driving provides a systematic way of constructing a control protocol to approximately suppress the excitations resulting from changing some parameter(s) of a quantum system at a finite rate. However, designing CD protocols typically requires knowledge of the original Hamiltonian . In this work, we design local CD driving protocols in Krylov space using only the characteristic local time scales of the system set by e.g., phonon frequencies in materials or Rabi frequencies in superconducting qubit arrays. Surprisingly, we find that convergence of these universal protocols is controlled by the asymptotic high-frequency tails of the response functions. This finding hints at a deep connection between the long-time, low-frequency response of the system controlling non-adiabatic effects, and the high-frequency response determined by the short-time operator growth and the Krylov complexity. We make this connection concrete by showing how, for a representative integrable model, we may extract long-time universal behavior of the correlation functions from a short-time expansion of the dynamics using a system-independent universal protocol. 

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5. Polynomial-Time Axioms of Choice and Polynomial-Time Cardinality

   https://doi.org/10.1007/s00224-023-10118-y  

   Grochow, Joshua A. (May 2023, Theory of Computing Systems)

   Abstract There is no single canonical polynomial-time version of the Axiom of Choice (AC); several statements of AC that are equivalent in Zermelo-Fraenkel (ZF) set theory are already inequivalent from a constructive point of view, and are similarly inequivalent from a complexity-theoretic point of view. In this paper we show that many classical formulations of AC, when restricted to polynomial time in natural ways, are equivalent to standard complexity-theoretic hypotheses, including several that were of interest to Selman. This provides a unified view of these hypotheses, and we hope provides additional motivation for studying some of the lesser-known hypotheses that appear here. Additionally, because several classical forms of AC are formulated in terms of cardinals, we develop a theory of polynomial-time cardinality. Nerode & Remmel (Contemp. Math.106, 1990 and Springer Lec. Notes Math. 1432, 1990) developed a related theory, but restricted to unary sets. Downey (Math. Reviews MR1071525) suggested that such a theory over larger alphabets could have interesting connections to more standard complexity questions, and we illustrate some of those connections here. The connections between AC, cardinality, and complexity questions also allow us to highlight some of Selman’s work. We hope this paper is more of a beginning than an end, introducing new concepts and raising many new questions, ripe for further research. 

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