Asymptotic Safety in Gauge Theories beyond Four Dimensions: Perturbative Tests and Fixed-Point Mergers
Abstract
Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop MS̅ beta function continued to D=4+2ε, we determine the largest dimension Dpt=4+2εpt below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map Dpt over color and flavor numbers for fermions in the fundamental representation of SU(N). At D=5, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the MS̅ series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet--infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding Nfcr≃ 2.09 N at large N in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color--flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer 2≤ N≤15 and 0≤ Nf/N≤11/2. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.
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BibTeX
@misc{deandrea2026asymptotic,
title = {{Asymptotic Safety in Gauge Theories beyond Four Dimensions: Perturbative Tests and Fixed-Point Mergers}},
author = {Aldo Deandrea and Jie Liu and Roman Pasechnik and Zhi-Wei Wang and Yu-Bo Zhao},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12225},
eprint = {2610.12225},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05829966v1},
}
RIS
TY - UNPB
TI - Asymptotic Safety in Gauge Theories beyond Four Dimensions: Perturbative Tests and Fixed-Point Mergers
AU - Aldo Deandrea
AU - Jie Liu
AU - Roman Pasechnik
AU - Zhi-Wei Wang
AU - Yu-Bo Zhao
PY - 2026
DA - 2026/10/08
PB - HAL
DO - 10.48550/arxiv.2610.12225
UR - https://hal.science/hal-05829966v1
AB - Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop MS̅ beta function continued to D=4+2ε, we determine the largest dimension D_pt=4+2ε_pt below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map D_pt over color and flavor numbers for fermions in the fundamental representation of SU(N). At D=5, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the MS̅ series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet--infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding N_f^cr≃ 2.09 N at large N in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color--flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer 2≤ N≤15 and 0≤ N_f/N≤11/2. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.
ER -