The paper by N. A. Nekrasov and S. L. Shatashvili explores the connection between four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories in the $\Omega$-background and quantum integrable systems. The $\Omega$-background introduces a deformation parameter $\varepsilon$, which is identified with the Planck constant in the quantum system. The supersymmetric vacua of the gauge theory are shown to correspond to the Bethe states of the quantum integrable system, with the twisted chiral ring maps to quantum Hamiltonians. The authors provide a detailed analysis of the $\Omega$-deformation, including the calculation of the twisted superpotential, and illustrate their results with examples such as the periodic Toda chain, the elliptic Calogero-Moser system, and the Hitchin system. They also discuss the quantization of the Hitchin system and present thermodynamic Bethe ansatz-like formulae for the spectra of commuting Hamiltonians. The paper aims to establish a novel link between gauge theories and quantum integrable systems, providing a unified framework for understanding both areas.The paper by N. A. Nekrasov and S. L. Shatashvili explores the connection between four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories in the $\Omega$-background and quantum integrable systems. The $\Omega$-background introduces a deformation parameter $\varepsilon$, which is identified with the Planck constant in the quantum system. The supersymmetric vacua of the gauge theory are shown to correspond to the Bethe states of the quantum integrable system, with the twisted chiral ring maps to quantum Hamiltonians. The authors provide a detailed analysis of the $\Omega$-deformation, including the calculation of the twisted superpotential, and illustrate their results with examples such as the periodic Toda chain, the elliptic Calogero-Moser system, and the Hitchin system. They also discuss the quantization of the Hitchin system and present thermodynamic Bethe ansatz-like formulae for the spectra of commuting Hamiltonians. The paper aims to establish a novel link between gauge theories and quantum integrable systems, providing a unified framework for understanding both areas.