Scalar Gauss-Bonnet Wormholes and the Imaginary Distance Bound
Abstract
We study O(4) symmetric Euclidean wormholes in four-dimensional gravity with a massless scalar linearly coupled to the Gauss-Bonnet invariant. At nonzero coupling, the Einstein wormhole becomes a regular complex saddle that satisfies the Kontsevich-Segal-Witten criterion until its branch ends at a finite coupling. In asymptotically flat space, the Gauss-Bonnet term modifies the scalar displacement and the on-shell action for finite wormholes, but the size dependent parts of both corrections vanish in the large throat limit. The original imaginary distance threshold therefore remains unchanged. A negative cosmological constant already lowers the Einstein large throat imaginary distance relative to its flat space value. When the Gauss-Bonnet coupling is also present, the scalar is no longer a modulus as it develops a logarithmic running and its trajectory has infinite length. Subtracting the logarithmic asymptotic behavior leaves a finite regulated displacement. Its large throat value is shifted upward from the Einstein AdS result by the Gauss-Bonnet interaction and determines the leading large charge behavior of the renormalized fixed charge action.
Related
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BibTeX
@misc{kehagias2026scalar,
title = {{Scalar Gauss-Bonnet Wormholes and the Imaginary Distance Bound}},
author = {Alex Kehagias and Antonio Riotto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28456},
eprint = {2609.28456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28456},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scalar Gauss-Bonnet Wormholes and the Imaginary Distance Bound
AU - Alex Kehagias
AU - Antonio Riotto
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28456
UR - https://arxiv.org/abs/2609.28456
AB - We study O(4) symmetric Euclidean wormholes in four-dimensional gravity with a massless scalar linearly coupled to the Gauss-Bonnet invariant. At nonzero coupling, the Einstein wormhole becomes a regular complex saddle that satisfies the Kontsevich-Segal-Witten criterion until its branch ends at a finite coupling. In asymptotically flat space, the Gauss-Bonnet term modifies the scalar displacement and the on-shell action for finite wormholes, but the size dependent parts of both corrections vanish in the large throat limit. The original imaginary distance threshold therefore remains unchanged. A negative cosmological constant already lowers the Einstein large throat imaginary distance relative to its flat space value. When the Gauss-Bonnet coupling is also present, the scalar is no longer a modulus as it develops a logarithmic running and its trajectory has infinite length. Subtracting the logarithmic asymptotic behavior leaves a finite regulated displacement. Its large throat value is shifted upward from the Einstein AdS result by the Gauss-Bonnet interaction and determines the leading large charge behavior of the renormalized fixed charge action.
ER -