Picard–Lefschetz theory and dilating ℂ*-actions by Seidel, Paul Alfred

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Lorentzian path integral for quantum tunneling and WKB approximation for wave-function by Hiroki Matsui

“…Abstract Recently, the Lorentzian path integral formulation using the Picard–Lefschetz theory has attracted much attention in quantum cosmology. …”
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High-precision numerical estimates of the Mellin-Barnes integrals for the structure functions based on the stationary phase contour by Sidorov Alexander, Solovtsova Olga, Lashkevich Vasil

“…We show that the Q2 evolution of the structure function can be represented as an integral over the contour of the stationary phase within the framework of the Picard-Lefschetz theory. The universality of the asymptotic contour of the stationary phase defined at some fixed value of the momentum transfer square Q02$Q_{0}^{2}$ for calculations with any Q2 is shown.…”
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Complex saddles and Euclidean wormholes in the Lorentzian path integral by Gregory J. Loges, Gary Shiu, Nidhi Sudhir

“…Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. …”
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A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations by Jun Nishimura, Katsuta Sakai, Atis Yosprakob

“…Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. …”
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Constraints on sequential discontinuities from the geometry of on-shell spaces by Holmfridur S. Hannesdottir, Andrew J. McLeod, Matthew D. Schwartz, Cristian Vergu

“…To establish our results, we review elements of Picard-Lefschetz theory, which connect the homotopy properties of the space of complexified external momenta to the homology of the combined space of on-shell internal and external momenta. …”
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Cutkosky rules and unitarity (violation) in D-instanton amplitudes by Ashoke Sen

“…Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories.…”
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Stokes Phenomena in Lensing by Xun Shi

“…As lensing of coherent astrophysical sources, e.g., pulsars, fast radio bursts, and gravitational waves, becomes observationally relevant, the mathematical framework of Picard–Lefschetz theory has recently been introduced to fully account for wave optics effects. …”
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Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations by Genki Fujisawa, Jun Nishimura, Katsuta Sakai, Atis Yosprakob

“…Abstract The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. …”
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Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves by Zhihao Duan, Jie Gu, Yasuyuki Hatsuda, Tin Sulejmanpasic

“…We hint at the possibility of exact 2-instanton solutions responsible for such contributions via Picard-Lefschetz theory. We also present a powerful way to compute the perturbative fluctuations around the 1-instanton saddle as well as the instanton-anti-instanton ambiguity by using the topological string formulation.…”
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Real-time quantum dynamics, path integrals and the method of thimbles by Zong-Gang Mou, Paul M. Saffin, Anders Tranberg, Simon Woodward

“…One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the complex plane, where the integral is better behaved. …”
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Remote Hawking-Moss instanton and the Lorentzian path integral by Daiki Saito, Naritaka Oshita

“…We consider a linear potential, which allows for analytic treatments, and evaluate the up-tunneling probability of a homogeneous scalar field in de Sitter spacetime. The Picard-Lefschetz theory is employed to identify the relevant Lefschetz thimble, representing the relevant tunneling trajectory. …”
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Functional methods for false-vacuum decay in real time by Wen-Yuan Ai, Björn Garbrecht, Carlos Tamarit

“…For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest- descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. …”
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Critical points at infinity, non-Gaussian saddles, and bions by Alireza Behtash, Gerald V. Dunne, Thomas Schäfer, Tin Sulejmanpasic, Mithat Ünsal

“…Abstract It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of Picard-Lefschetz theory. In this work we compute the contribution from non-BPS multi-instanton configurations, such as instanton-anti-instanton ℐℐ¯ $$ \left[\mathrm{\mathcal{I}}\overline{\mathrm{\mathcal{I}}}\right] $$ pairs, and argue that these contributions should be interpreted as exact critical points at infinity. …”
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Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D N $$ \mathcal{N} $$ = 2 field theories by Daniele Dorigoni, Philip Glass

“…This effectively introduces a hidden “topological angle” into the theory and the path integral can be now decomposed into a sum over different topological sectors via Picard-Lefschetz theory. The second problem is solved by deforming the matter content making manifest the Cheshire Cat resurgence structure of the supersymmetric theory, allowing us to reconstruct non-perturbative information from perturbative data even when these do truncate.…”
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