I saw in a lecture about O(3) sigma model something about 'target manifold', but I do not know what is it.
Is there any book I could learn about that?
2026-04-09 03:59:57.1775707197
What is 'target manifold'?
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As James S. Cook suggests in comments, the wikipedia entry will get you started.
In general in a sigma model, one considers maps from some collection of manifolds, often Riemann surfaces, to some fixed "target manifold".
The physical picture, at least in string theory, is that the target manifold is space-time, and the Riemann surface mapping to it is the world-sheet of some string moving through space-time.
In string theory the target manifold is often taken to be usual Lorentzian space-time (so $\mathbb R^4$) times a $3$-complex-dimensional Calabi-Yau variety (these are the "extra dimensions" of space-time that appear in string theory).