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Modular invariance

Index Modular invariance

In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. [1]

Table of Contents

  1. 11 relations: Global anomaly, Gravitational anomaly, Group (mathematics), Large diffeomorphism, Modular form, Modular group, One-loop Feynman diagram, String theory, Theoretical physics, Torus, Two-dimensional conformal field theory.

Global anomaly

In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory.

See Modular invariance and Global anomaly

Gravitational anomaly

In theoretical physics, a gravitational anomaly is an example of a gauge anomaly: it is an effect of quantum mechanics — usually a one-loop diagram—that invalidates the general covariance of a theory of general relativity combined with some other fields.

See Modular invariance and Gravitational anomaly

Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element. Modular invariance and group (mathematics) are Symmetry.

See Modular invariance and Group (mathematics)

Large diffeomorphism

In mathematics and theoretical physics, a large diffeomorphism is an equivalence class of diffeomorphisms under the equivalence relation where diffeomorphisms that can be continuously connected to each other are in the same equivalence class. Modular invariance and large diffeomorphism are theoretical physics stubs.

See Modular invariance and Large diffeomorphism

Modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane, \,\mathcal\,, that satisfies.

See Modular invariance and Modular form

Modular group

In mathematics, the modular group is the projective special linear group \operatorname(2,\mathbb Z) of matrices with integer coefficients and determinant 1.

See Modular invariance and Modular group

One-loop Feynman diagram

In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic).

See Modular invariance and One-loop Feynman diagram

String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

See Modular invariance and String theory

Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena.

See Modular invariance and Theoretical physics

Torus

In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.

See Modular invariance and Torus

Two-dimensional conformal field theory

A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations.

See Modular invariance and Two-dimensional conformal field theory

References

[1] https://en.wikipedia.org/wiki/Modular_invariance