Quantization, i.e. the passage from classical mechanics to quantum mechanics, is known to be somewhat ambiguous. Geometric quantization is a mathematical tool to solve this problem. It is currently known as the Kostant-Souriau procedure (for a survey see e.g. [M. Vergne, Astérisque 282, 249-278, Exp. No. 888 (2002; Zbl 1037.53062)]). Since its initial formulation by J.-M. Souriau [Commun. Math. Phys. 1, 374–398 (1966; Zbl 1148.81307)] in 1966 many researchers contributed to geometric quantization, and E. Witten is one of them. Mathematically, the classical phase space is a symplectic manifold \((M,\omega)\). The process of prequantization provides a Hermitian line bundle \(L\) over \(M\), equipped with a \(U(1)\) connection with curvature \(i\omega\) and referred to as the prequantum line bundle. Further steps are named polarization and metaplectic correction. The present article opens a new perspective on quantization, based on two-dimensional sigma models, by passing to the a complexification \(Y\) of \(M\). Of great interest here is the fact that \(Y\) is an affine variety. However, it is not clear whether the new perspective helps in concrete cases, e.g. in performing computations and getting new formulas. In this framework, quantization is performed via branes, that is, the Hilbert space of a quantum model is obtained by quantizing \((M,\omega)\) as a space of \((B,B')\) strings, where \(B\) and \(B'\) are two \(A\)-branes. The choice of \(B\) is determined by \(\omega\). As an example, the authors describe in another way the representations of the group \(SL(2,\mathbb{R})\). The new method is also applied to the Chern-Simons gauge theory. The question remains: do we really get a valid systematic theory of quantization this way?