A No-Go Theorem for Nonspherical Bounces with a Single Negative Mode
Abstract
False vacuum decay is conventionally described by a spherically symmetric bounce with a single negative fluctuation mode. This raises a fundamental question: can the single negative mode requirement itself enforce spherical symmetry, independently of action minimization? For a single real scalar field with a smooth potential in flat spacetime, we rigorously prove that every localized nonspherical saddle with zero initial velocity has at least three negative modes. Additional reflection symmetries further tighten these bounds, as illustrated in a sextic scalar model. Our findings exclude nonspherical bounce candidates with a single negative mode, providing a complementary spectral foundation for the spherical bounce description of false vacuum decay.
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BibTeX
@misc{chen2026nogo,
title = {{A No-Go Theorem for Nonspherical Bounces with a Single Negative Mode}},
author = {Guangshang Chen and Jianpeng Dai and Yang Xiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16688},
eprint = {2610.16688},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16688},
}
RIS
TY - UNPB
TI - A No-Go Theorem for Nonspherical Bounces with a Single Negative Mode
AU - Guangshang Chen
AU - Jianpeng Dai
AU - Yang Xiao
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16688
UR - https://arxiv.org/abs/2610.16688
AB - False vacuum decay is conventionally described by a spherically symmetric bounce with a single negative fluctuation mode. This raises a fundamental question: can the single negative mode requirement itself enforce spherical symmetry, independently of action minimization? For a single real scalar field with a smooth potential in flat spacetime, we rigorously prove that every localized nonspherical saddle with zero initial velocity has at least three negative modes. Additional reflection symmetries further tighten these bounds, as illustrated in a sextic scalar model. Our findings exclude nonspherical bounce candidates with a single negative mode, providing a complementary spectral foundation for the spherical bounce description of false vacuum decay.
ER -