Recently a detailed correspondence was established between, on one side, four and five-dimensional large-N supersymmetric gauge theories with $\mathcal{N}=2$ supersymmetry and adjoint matter, and, on the other side, integrable 1+1-dimensional quantum hydrodynamics. Under this correspondence the phenomenon of dimensional transmutation, familiar in asymptotically free QFTs, gets mapped to the transition from the elliptic Calogero-Moser many-body system to the closed Toda chain. In this paper we attempt to formulate the hydrodynamical counterpart of the dimensional transmutation phenomenon inspired by the identification of the periodic Intermediate Long Wave (ILW) equation as the hydrodynamical limit of the elliptic Calogero-Moser/Ruijsenaars-Schneider system. We also conjecture that the chiral flow in the vortex fluid provides the proper framework for the microscopic description of such dimensional transmutation in the 1+1d hydrodynamics. We provide a geometric description of this phenomenon in terms of the ADHM moduli space.

中文翻译：

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1+1D量子流体力学中的维嬗变

最近，在具有 $\mathcal{N}=2$ 超对称性和伴随物质的四维和五维大 N 超对称规范理论之间建立了详细的对应关系，另一方面，可积 1+1-维量子流体力学。在这种对应关系下，渐近自由 QFT 中常见的维度嬗变现象被映射到从椭圆 Calogero-Moser 多体系统到封闭 Toda 链的过渡。在本文中，我们尝试制定维度嬗变现象的流体动力学对应物，其灵感来自于将周期性中长波 (ILW) 方程识别为椭圆 Calogero-Moser/Ruijsenaars-Schneider 系统的流体动力学极限。我们还推测涡流中的手征流为 1+1d 流体动力学中这种维度嬗变的微观描述提供了适当的框架。我们根据 ADHM 模空间提供了这种现象的几何描述。