Complex Worldline Instantons in (Anti-)de Sitter Space
Abstract
We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio $R |eE|/m$ (R being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.
Related
- Boundary Conditions and Entanglement in Anti-de Sitter Space
- Finite Spectral Recurrences for Loop Integrals in de Sitter and Anti-de Sitter Space
- Post-Newtonian theory in de Sitter and anti-de Sitter spacetimes
- Semiclassical Cosmological Constant in Anti-de Sitter and de Sitter Spacetimes
- Tidal Love Numbers of Thin-Shell Wormholes, de Sitter Gravastars, and Anti-de Sitter Gravastars via Full Perturbed Junction Conditions
BibTeX
@misc{castellano2026complex,
title = {{Complex Worldline Instantons in (Anti-)de Sitter Space}},
author = {Alberto Castellano and Jinwei Chu and Eliseu Kloster and Jamie A. P. Law-Smith},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03862},
eprint = {2610.03862},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03862},
}
RIS
TY - UNPB
TI - Complex Worldline Instantons in (Anti-)de Sitter Space
AU - Alberto Castellano
AU - Jinwei Chu
AU - Eliseu Kloster
AU - Jamie A. P. Law-Smith
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03862
UR - https://arxiv.org/abs/2610.03862
AB - We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio $R |eE|/m$ (R being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.
ER -