U-duality

U-duality is a symmetry of string theory

String theory

String theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity...

 or M-theory

M-theory

In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds the dimensionality of five superstring theories in 10 dimensions, it is believed that the 11-dimensional theory unifies all string theories...

 combining S-duality

S-duality

In theoretical physics, S-duality is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling constant in one theory to states and vacua with coupling constant in the dual theory...

 and T-duality

T-duality

T-duality is a symmetry of string theory relating small and large distances. T-duality is not present in ordinary particle theory, indicating that strings experience spacetime in a way that is fundamentally distinct than the way particles do. It relates different string theories that were thought...

 transformations. The term is most often met in the context of the "U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold

Topological manifold

In mathematics, a topological manifold is a topological space which looks locally like Euclidean space in a sense defined below...

). This is the union of all the S- and T-dualities available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example.

U-duality is a symmetry of string theory

String theory

String theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum theory of gravity...

 or M-theory

M-theory

In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds the dimensionality of five superstring theories in 10 dimensions, it is believed that the 11-dimensional theory unifies all string theories...

 combining S-duality

S-duality

In theoretical physics, S-duality is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling constant in one theory to states and vacua with coupling constant in the dual theory...

 and T-duality

T-duality

T-duality is a symmetry of string theory relating small and large distances. T-duality is not present in ordinary particle theory, indicating that strings experience spacetime in a way that is fundamentally distinct than the way particles do. It relates different string theories that were thought...

 transformations. The term is most often met in the context of the "U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold

Topological manifold

In mathematics, a topological manifold is a topological space which looks locally like Euclidean space in a sense defined below...

). This is the union of all the S- and T-dualities available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example.