skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Deep learning beyond Lefschetz thimbles

; ; ;
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
FG02-95ER40907; FG02-93ER-40762
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 9; Related Information: CHORUS Timestamp: 2017-11-10 10:06:45; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Deep learning beyond Lefschetz thimbles. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.094505.
Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, & Lawrence, Scott. Deep learning beyond Lefschetz thimbles. United States. doi:10.1103/PhysRevD.96.094505.
Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Fri . "Deep learning beyond Lefschetz thimbles". United States. doi:10.1103/PhysRevD.96.094505.
title = {Deep learning beyond Lefschetz thimbles},
author = {Alexandru, Andrei and Bedaque, Paulo F. and Lamm, Henry and Lawrence, Scott},
abstractNote = {},
doi = {10.1103/PhysRevD.96.094505},
journal = {Physical Review D},
number = 9,
volume = 96,
place = {United States},
year = {Fri Nov 10 00:00:00 EST 2017},
month = {Fri Nov 10 00:00:00 EST 2017}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 10, 2018
Publisher's Accepted Manuscript

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using amore » simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.« less
  • Cited by 19
  • Cited by 8
  • We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.
  • Here, we smore » how that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the “separation” quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study N = 2 extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton-anti-instanton amplitude (naively calculated) seems to contribute to the ground state energy. We show, however, that the instanton-anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively of the same sign and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles due to their relative Hidden Topological Angles (HTAs). This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescription for higher order semi-classics, but a necessary one. This deduction seems to be universal and applicable to both supersymmetric and non-supersymmetric theories. In conclusion we speculate that similar conspiracies are responsible for the non-formation of certain molecular contributions in theories where instantons have more than two fermionic zeromodes and do not contribute to the superpotential.« less