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). Theoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, predicting physical phenomena through a physical theory. There are three types of theories in physics; mainstream theories, proposed theories and fringe theories. ... In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space. ... In advanced theoretical physics, a modulus is a scalar field with no potential energy. ... In particle physics, supersymmetry is a hypothetical symmetry that relates bosons and fermions. ... In theoretical physics, a supercharge is a generator of supersymmetry transformations. ...

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 algebraic geometry, the moduli problem is to describe the parameters on which algebraic varieties depend. ...

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. A string theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. ... In mathematics, a manifold M is a type of space, characterized in one of two equivalent ways: near every point of the space, we have a coordinate system; or near every point, the environment is like that in Euclidean space of a given dimension. ... In mathematics, a Calabi-Yau manifold is a compact K hler manifold with a vanishing first Chern class. ... In gauge theory, a Wilson loop is a gauge-invariant observable obtained from the holonomy of the gauge connection around a given loop. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, a coupling constant, usually denoted , is a number that determines the strength of an interaction. ...

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. In algebraic geometry, the moduli problem is to describe the parameters on which algebraic varieties depend. ... In classical algebraic geometry (and to some extent also in modern algebraic geometry), the main objects of study are algebraic varieties. ... In mathematics, compactification is applied to topological spaces to make them compact spaces. ...

Another example in string theory is the dilaton (the coupling constant). In theoretical physics, dilaton originally referred to a theoretical scalar field; as a photon refers in one sense to the electromagnetic field. ...

See also vacuum manifold. In quantum field theory, the vacuum state may be degenerate. ...