论文标题
关于变形的阳米尔斯理论的扰动方面
On the perturbative aspects of deformed Yang-Mills theory
论文作者
论文摘要
$ \ mathbb {r}^3 \ times s^1 $上的中心稳定的$ su（n）$ yang-mills理论是类似QCD的理论，可以通过使用$ s^1 $ circle Length Lugh $ circle $ l $来设计，以在所有能量尺度上保持弱耦合。在这种制度中，这些理论承认有效的长距离描述为$ \ mathbb {r}^3 $上的Abelian $ u（1）^{n-1} $量学理论，并且可以可靠地利用半经典来研究非扰动现象，例如色彩约束和分析设置中的质量差异。在扰动树级别，长距离有效理论包含$（n-1）$的免费光子，带有相同的量规耦合$ g^2_3 \ equiv g^2/l $。真空极化效果从整合沉重的充电场上，提高这种退化，从而给出$ \ floes {\ frac {n} {2}} $不同的值：$ g^2（\ frac {2} {l} {l} {l} {l} {l} {l} {l} {l}） In this work, we calculate these corrections to one-loop order in theories where the centre-symmetric vacuum is stabilised by $2\leq n_f \leq 5$ massive adjoint Weyl fermions with masses of order $m_λ\sim \frac{2π}{NL}$, (also known as "deformed Yang-Mills,") and show that our results agree with those found in previous studies in $m_λ\至0 $限制。然后，我们证明我们的结果具有直观的解释，因为在$ n \ to \ infty $，field-$ nl $ limit中，在非扰动“新兴晶格的第四维”的背景下，在“晶格动量”中的耦合。
Centre-stabilised $SU(N)$ Yang-Mills theories on $\mathbb{R}^3 \times S^1$ are QCD-like theories that can be engineered to remain weakly-coupled at all energy scales by taking the $S^1$ circle length $L$ to be sufficiently small. In this regime, these theories admit effective long-distance descriptions as Abelian $U(1)^{N-1}$ gauge theories on $\mathbb{R}^3$, and semiclassics can be reliably employed to study non-perturbative phenomena such as colour confinement and the generation of mass gaps in an analytical setting. At the perturbative tree level, the long-distance effective theory contains $(N-1)$ free photons with identical gauge couplings $g^2_3 \equiv g^2/L$. Vacuum polarisation effects, from integrating out heavy charged fields, lift this degeneracy to give $\floor{\frac{N}{2}}$ distinct values: $g^2(\frac{2}{L})\lesssim g_{3,\ell}^2 L \lesssim g^2(\frac{2π}{NL}) $. In this work, we calculate these corrections to one-loop order in theories where the centre-symmetric vacuum is stabilised by $2\leq n_f \leq 5$ massive adjoint Weyl fermions with masses of order $m_λ\sim \frac{2π}{NL}$, (also known as "deformed Yang-Mills,") and show that our results agree with those found in previous studies in the $m_λ\to 0$ limit. Then, we show that our result has an intuitive interpretation as the running of the coupling in a "lattice momentum" in the context of the non-perturbative "emergent latticised fourth dimension" in the $N\to \infty$, fixed-$NL$ limit.
