杨-米尔斯理论中的混沌
Chaos in Yang-Mills
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中文总结 AI 辅助
该研究探究纯规范SU(N)的混沌特性，发现其仅在非阿贝尔且空间维数d>2时出现，通过空间威尔逊环大小施加截断揭示临界直径处的scrambling转变，需进一步研究其物理意义。
中文摘要 AI 辅助
我们通过空间威尔逊环的时间演化研究纯规范SU(N)的动力学。我们在弱't Hooft耦合与大N极限下计算其时序外关联函数，并提出强耦合描述的框架。我们发现，纯规范杨-米尔斯理论中的算符仅在群为非阿贝尔且空间维数d>2时增长，由此推测纯规范理论仅在非阿贝尔且d>2时才会出现混沌。即使在弱耦合下，关联函数的指数仍继承了胶子自能虚部的红外敏感性，该敏感性依赖于非微扰磁标度。我们随后探究了环自身大小提供该标度的可能性，因为环算符对软于1/2R的动量无响应。通过这种方式施加截断后，指数在临界直径处改变符号：更小的环会发生 scrambling（ scrambling指量子信息混乱化），更大的环则不会，且在临界点处scrambling时间发散。该转变源于上述截断。要确定该转变是否具有物理意义，还需进一步研究，特别是对热衰变宽度的第一性原理处理。
英文摘要
We study the dynamics of pure-gauge SU(N) through the time evolution of a spatial Wilson loop. We compute its out-of-time-order correlator at weak 't Hooft coupling and large N, and propose a framework for the strong-coupling description. We find that operators in pure-gauge Yang-Mills grow only when the group is non-abelian and d>2, and conjecture that pure gauge theories are chaotic only when non-abelian at d>2. Even at weak coupling the correlator's exponent inherits the IR sensitivity of the gluon self-energy imaginary part, which rests on the non-perturbative magnetic scale. We then explore the possibility that the loop's own size supplies that scale, since the loop operator is blind to any momenta softer than 1/2R. With the cutoff imposed that way the exponent changes sign at a critical diameter: smaller loops scramble, larger ones do not, and the scrambling time diverges at the crossing. The transition follows from that cutoff. Further investigation, in particular a first-principles treatment of the thermal decay width, is required to establish whether it is physical.
