Moduli
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In theoretical physics, moduli are scalar fields whose different values are equally good (each one such scalar field is called a modulus). The reason is that the potential energy for moduli is constant, which can be guaranteed, for example, by supersymmetry (with sufficiently many supercharges).
The space of possible configurations (values) of all these moduli is called the moduli space (that page gives some explanation of the original, mathematical usage).
In string theory, one can imagine the moduli to parameterize not only the allowed shape of the internal manifold (e.g. the Calabi-Yau manifold) which is the usual meaning of the term "moduli space" in mathematics, but also the Wilson lines of the gauge fields around non-trivial cycles, various coupling constants, and so forth.
On the other hand, the usage of the phrase "moduli space" in mathematics is more general in the sense that the moduli describe the shape of an arbitrary algebraic variety, not necessarily a manifold relevant for compactification in string theory.
Another example in string theory is the dilaton (the coupling constant).
See also vacuum manifold.Template:Physics-stub