将4−ε维厄米特场论与轴子耦合费米子的$\u001cPT\u001d$对称理论联系起来的重整化群流
Renormalisation group flows connecting a $4-ε$ dimensional Hermitian field theory to a $\mathcal{PT}$-symmetric theory for a fermion coupled to an axion
AI总结：
该研究在4−ε维下证明厄米特轴子-费米子耦合场论的重整化群流可通向非厄米特PT对称理论，通过多圈微扰与ε展开验证结果，并发现3维下可能存在非微扰PT对称鞍点。
摘要：
研究表明，在时空维度$D=4-ε$（其中$ε>0$）下，厄米特场论的重整化群流存在通向非厄米特宇称-时间（$\u001cPT\u001d$）对称场论的轨迹，该理论描述轴子与费米子的耦合体系。在这个可重整化场论中，狄拉克费米子场与赝标量（轴子）场存在汤川耦合$g$，且赝标量场存在四次自耦合$u$。通过分析依赖$ε$的Wilson-Fisher不动点之间的流，同时对汤川耦合计算至**三圈**阶、对四次标量耦合计算至**两圈**阶，验证了这一发现的稳健性。研究结合微扰分析与$ε$展开，计算了非平凡不动点邻域的流。全局流模式显示流从正$u$流向负$u$；实$g$与虚$g$之间不存在流。借助求和技术，研究证明了$D=3$时可能存在非微扰的$\u001cPT\u001d$对称鞍点。
英文摘要：
The renormalisation group flow of a Hermitian field theory is shown to have trajectories which lead to a non-Hermitian Parity-Time ($\mathcal{PT}$) symmetric field theory for an axion coupled to a fermion in spacetime dimensions $D=4-ε$, where $ε>0 $. In this renormalisable field theory, the Dirac fermion field has a Yukawa coupling $g$ to a pseudoscalar (axion) field and there is quartic pseudoscalar self-coupling $u$. The robustness of this finding is established by considering flows between $ε$ dpependent Wilson-Fisher fixed points and also by working to \emph{three loops} in the Yukawa coupling and to \emph{two loops} in the quartic scalar coupling. The flows in the neighbourhood of the non-trivial fixed points are calculated using perturbative analysis, together with the $ε$ expansion. The global flow pattern indicates flows from positive $u$ to negative $u$; there are no flows between real and imaginary $g$. Using summation techniques we demonstrate a possible non-perturbative $\mathcal{PT}$-symmetric saddle point for $D=3$.
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