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A bstract In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we study specific examples, including the Möbius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models. We find that metrics for optimal path integrals coincide with particular slices of AdS 3 geometries, on which Einstein’s equations are equivalent to the condition for minimal path integral complexity. We also find that while leading divergences of path integral complexity remain unchanged, constant contributions are modified in a universal, position dependent manner. Moreover, we analyze entanglement entropies in inhomogeneous CFTs and show that they satisfy Hill’s equations, which can be used to extract the energy density consistent with the first law of entanglement. Our findings not only support comparisons between slices of bulk spacetimes and circuits of path integrations, but also demonstrate that path integral geometries and complexity serve as a powerful tool for understanding the interesting physics of inhomogeneous systems.

A bstract We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos algorithm and evaluate the Krylov complexity of simple operators (primaries and the stress tensor) under a unitary evolution protocol. Evolution of primary operators proceeds as a flow into the ‘bath of descendants’ of the Verma module. These descendants are labeled by integer partitions and have a one-to-one map to Young diagrams. This relationship allows us to rigorously formulate operator growth as paths spreading along the Young’s lattice. We extract quantitative features of these paths and also identify the one that saturates the conjectured upper bound on operator growth.

Background/Objectives: The primary aim of this systematic review was to evaluate fertility outcomes and the oncological safety of different surgical techniques of radical trachelectomy (RT). Methods: The systematic review was performed in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. A systematic literature search on PubMed, Embase, and Google Scholar was performed between 1 November 2023 and 31 March 2024 with no limits for the time of publication. Results: In total, 56 studies met the inclusion criteria: 22 for abdominal RT (1712 patients), 14 for endoscopic RT (445 patients), and 22 for vaginal RT (1158 patients). Data regarding certain steps of the procedure (uterine artery preservation, autonomous nerve-sparing, abdominal cerclage, types of sutures used for the cerclage, uterine dilatation during cerclage placement, prolongation of uterine catheterization, type of uterovaginal anastomosis, antibiotic prophylaxis, and suppression of menstruation) were extracted and analyzed with regard to the obstetrical and oncological outcomes. Endoscopic RT was associated with a significantly higher pregnancy rate and a lower rate of preterm deliveries. Uterine artery preservation was associated with a higher live birth rate. Nerve-sparing RT resulted in a higher pregnancy rate, but no differences in the attempt for pregnancy and live birth rates were observed. Conclusions: Taking into account the obstetrical outcomes, it seems that the preferred option for radical RT is an endoscopic procedure with preservation of the uterine artery and the pelvic autonomic nerves. However, the safety of the endoscopic approach should be evaluated in prospective trials.

A bstract We study four-dimensional quantum gravity with negative cosmological constant in the minisuperspace approximation and compute the partition function for the S 3 boundary geometry. In this approximation scheme the path integrals become dominated by a class of asymptotically AdS “microstate geometries.” Despite the fact that the theory is pure Einstein gravity without supersymmetry, the result precisely reproduces, up to higher curvature corrections, the Airy function in the S 3 partition function of the maximally supersymmetric Chern-Simons-matter (CSM) theory which sums up all perturbative 1 /N corrections. We also show that this can be interpreted as a concrete realization of the idea that the CFT partition function is a solution to the Wheeler-DeWitt equation as advocate in the holographic renormalization group. Furthermore, the agreement persists upon the inclusion of a string probe and it reproduces the Airy function in the vev of half-BPS Wilso loops in the CSM theory. These results may suggest that the supergravity path integrals localize to the minisuperspace in certain cases and the use of the minisuperspace approximation in AdS/CFT may be a viable approach to study 1 /N corrections to large N CFTs.

A bstract We consider time-dependent entanglement entropy (EE) for a 1+1 dimensional CFT in the presence of angular momentum and U(1) charge. The EE saturates, irrespective of the initial state, to the grand canonical entropy after a time large compared with the length of the entangling interval. We reproduce the CFT results from an AdS dual consisting of a spinning BTZ black hole and a flat U(1) connection. The apparent discrepancy that the holographic EE does not a priori depend on the U(1) charge while the CFT EE does, is resolved by the charge-dependent shift between the bulk and boundary stress tensors. We show that for small entangling intervals, the entanglement entropy obeys the first law of thermodynamics, as conjectured recently. The saturation of the EE in the field theory is shown to follow from a version of quantum ergodicity; the derivation indicates that it should hold for conformal as well as massive theories in any number of dimensions.

A bstract Pseudo-entropy and SVD entropy are generalizations of the entanglement entropy that involve post-selection. In this work we analyze their properties as measures on the spaces of quantum states and argue that their excess provides useful characterization of a difference between two (i.e. pre-selected and post-selected) states, which shares certain features and in certain cases can be identified as a metric. In particular, when applied to link complement states that are associated to topological links via Chern-Simons theory, these generalized entropies and their excess provide a novel quantification of a difference between corresponding links. We discuss the dependence of such entropy measures on the level of Chern-Simons theory and determine their asymptotic values for certain link states. We find that imaginary part of the pseudo-entropy is sensitive to, and can diagnose chirality of knots. We also consider properties of entropy measures for simpler quantum mechanical systems, such as generalized SU(2) and SU(1,1) coherent states, and tripartite GHZ and W states.

A bstract In this work we study families of generalised coherent states constructed from SL(2,R) subalgebras of the Virasoro algebra in two-dimensional conformal field theories. We derive the energy density and entanglement entropy and discuss their equivalence with analogous quantities computed in locally excited states. Moreover, we analyze their dual, holographic geometries and reproduce entanglement entropies from the Ryu-Takayanagi prescription. Finally, we outline possible applications of this universal class of states to operator growth and inhomogeneous quenches.

A bstract We consider sphere partition functions of TT deformed large N conformal field theories in d = 2, 3, 4, 5 and 6 dimensions, computed using the flow equation. These are shown to non-perturbatively match with bulk computations of AdS d +1 with a finite radial cut-off. We then demonstrate how the flow equation can be independently derived from a regularization procedure of defining TT operators through a local Callan-Symanzik equation. Finally, we show that the sphere partition functions, modulo bulk-counterterm contributions, can be reproduced from Wheeler-DeWitt wavefunctions.

A bstract In this work, we investigate local quench dynamics in two-dimensional conformal field theories using Krylov space methods. We derive Lanczos coefficients, spread complexity, and Krylov entropies for local joining and splitting quenches in theories on an infinite line, a circle, a finite interval, and at finite temperature. We examine how these quantities depend on the central charge of the underlying conformal field theory and find that both spread complexity and Krylov entropy are proportional to it. Interestingly, Krylov entropies evolve logarithmically with time, mirroring standard entanglement entropies, making them useful for extracting the central charge. In the large central charge limit, using holography, we establish a connection between the rate of spread complexity and the proper momentum of the tip of the end-of-the world brane, which probes the bulk analogously to a point particle. Our results further demonstrate that spread complexity and Krylov entropies are powerful tools for probing non-equilibrium dynamics of interacting quantum systems.