A gap between two approaches of dimensional reduction for a six-dimensional Kaluza-Klein theory

Abstract

Inspired by the five-dimensional Kaluza-Klein theory, we would like to study the dimensional reduction issue of six-dimensional Kaluza-Klein extension in this paper. In particular, we will examine two possible approaches of dimensional reduction from six-dimensional spacetimes to four-dimensional ones. The first one is a direct dimensional reduction, i.e., from six-dimensional spacetimes directly to four-dimensional ones, via a $T^2\equiv S^1\times S^1$ compactification, while the second one is an indirect dimensional reduction, i.e., from six-dimensional spacetimes to five-dimensional ones then four-dimensional ones, via two separated $S^1$ compactifications. Interestingly, we show that these two approaches lead to different four-dimensional effective actions although using the same six-dimensional metric. It could therefore address an important question of which approach is more reliable than the other.

16 pages. Accepted for publication in The European Physical Journal Plus (EPJ Plus). Comments are welcome

References in corpus (15)

• Dynamics of dark energy
• Consistent Kaluza-Klein Sphere Reductions
• Consistent nonlinear KK reduction of 11d supergravity on $Ad{S}_7\times S_4$ and self-duality in odd dimensions
• Consistency of the $Ad{S}_7\times S_4$ reduction and the origin of self-duality in odd dimensions
• Physics of String Flux Compactifications
• Multiple field inflation
• Internal space structure generalization of the quintom cosmological scenario
• Fermions in Kaluza-Klein and Randall-Sundrum Theories
• A Quintom scenario with mixed kinetic terms
• Quintessence dynamics with two scalar fields and mixed kinetic terms
• Anisotropic power-law inflation in a two-scalar-field model with a mixed kinetic term
• Anisotropic power-law inflation for a model of two scalar and two vector fields
• Kaluza-Klein Induced Gravity Inflation
• Kaluza-Klein Higher Derivative Induced Gravity
• Anisotropic power-law inflation for a generalized model of two scalar and two vector fields