KaluzaKleinModen

KaluzaKleinModen refers to the Kaluza-Klein modes that arise in theories with extra spatial dimensions that are compactified. These modes are the four-dimensional manifestations of higher-dimensional fields, appearing as a tower of states with increasing masses. The concept honors Theodor Kaluza, who first proposed unifying gravity and electromagnetism with an extra dimension, and Oskar Klein, who suggested the extra dimension could be compact and quantized.

In a simple setup with one extra dimension compactified on a circle of radius R, a field can be expanded into Fourier modes along the extra coordinate. Each mode behaves as a separate four-dimensional field, with a mass given by m_n^2 = m_0^2 + (n/R)^2, where m_0 is the field’s intrinsic four-dimensional mass and n is an integer. The n = 0 mode is often the familiar Standard Model field (or graviton, depending on the field), while n > 0 modes are heavier excitations called KK modes. For gauge fields and gravitons, the KK excitations appear as copies with higher mass, sometimes carrying distinct quantum numbers depending on the geometry and boundary conditions.

KK modes are central to many higher-dimensional models, including those with large extra dimensions or warped geometries. They can influence collider processes, precision measurements, and cosmology. In realistic constructions, the extra dimensions are often compactified on orbifolds or more complex manifolds, which can affect the spectrum and lead to phenomena such as chirality and zero modes for fermions. The properties and experimental signatures of Kaluza-KleinModen depend on the geometry, size of the extra dimensions, and the cutoff scale of the theory.