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arXiv 1908.11347hep-th
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标量场的大荷极限与$ε=0$上的Wilson-Fisher不动点

The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $ε=0$

G. Arias-Tamargo, D. Rodriguez-Gomez, J. G. Russo

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14 pages
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摘要：

我们研究了$4-ε$维中当耦合达到临界值$g\sim ε$时出现的$O(2)$ Wilson-Fisher不动点中的大电荷算符$ϕ^n$（$ϕ$是复化的标量场）的扇区.我们表明，在极限$g\to 0$，当理论天真地接近高斯不动点，在固定的$g\,n^2\equiv λ$与$n\to \infty $运营商的部门仍然是非平凡的。令人惊讶的是，人们可以计算出精确的2点函数，从而通过费曼图的完全重算来计算算子$ϕ^n$的非平凡反常维数。同样的结果可以从鞍点近似的路径积分，这部分地解释了极限的存在。最后，我们将这些结果推广到具有$(\barϕ\,ϕ)^3$势的三维$O(2)$对称理论。

英文摘要：

We study the sector of large charge operators $ϕ^n$ ($ϕ$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-ε$ dimensions that emerges when the coupling takes the critical value $g\sim ε$. We show that, in the limit $g\to 0$, when the theory naively approaches the gaussian fixed point, the sector of operators with $n\to \infty $ at fixed $g\,n^2\equiv λ$ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator $ϕ^n$ by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional $O(2)$-symmetric theory with $(\barϕ\,ϕ)^3$ potential.

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