Gauge structure of Yang-Mills theories with extra dimensions

Abstract

An effective Lagrangian for Yang-Mills theories with $n$ extra dimensions is constructed. We start from a field theory governed by the extra-dimensional Poincaré group $ISO(1,3+n)$ and the extended gauge group $SU(N,M^{4+n})$, characterized by an energy scale $\Lambda$ and assumed to be valid at energies far below this scale. Assuming that the size of the extra dimensions is much larger than the distance scale at which this theory is valid, an effective theory with symmetry groups $ISO(1,3)$ and $SU(N,M^4)$ is constructed. Such theories are connected by a canonical transformation that hides $ISO(1,3+n)\otimes SU(N,M^{4+n})$ into $ISO(1,3)\otimes SU(N,M^4)$, and endows the KK gauge fields with mass. Using a set of orthogonal functions $\{f^{(\underline{0})},f^{(\underline{m})}(\bar{x})\}$, generated by the Casimir invariant ${\bar{P}}^2$ associated with the translations subgroup $T(n)\subset ISO(n)$, the degrees of freedom of $ISO(1,3+n)\otimes SU(N,M^{4+n})$ are expanded via a general Fourier series, whose coefficients are the degrees of freedom of $ISO(1,3)\otimes SU(N,M^4)$. These functions, corresponding to the projection on the coordinates basis $\{|\bar{x}⟩\}$ of the discrete basis $\{|0⟩,|p^{(\underline{m})}⟩\}$ generated by ${\bar{P}}^2$, are central in defining the effective theory. Components along the base state $f^{(\underline{0})}=⟨\bar{x}|0⟩$, identified as the standard Yang-Mills fields, do not receive mass at the compactification scale; components along excited states $f^{(\underline{m})}=⟨\bar{x}|p^{(\underline{m})}⟩$, corresponding to KK excitations, receive mass at this scale. Associated with any direction $|p^{(\underline{m})}\ne 0⟩$ there are a massive gauge field and a pseudo-Goldstone boson. Resemblances of this mass-generating mechanism with the Brout-Englert-Higgs mechanism are stressed.

arXiv comment22 pages; this paper is a comprehensively revised and renewed version of arXiv arXiv:1603.03128

References in corpus (40)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Hierarchy Problem and New Dimensions at a Millimeter
• Particle Dark Matter: Evidence, Candidates and Constraints
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Dirichlet-Branes and Ramond-Ramond Charges
• String Theory Dynamics In Various Dimensions
• Heterotic and Type I String Dynamics from Eleven Dimensions
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Bounds on Universal Extra Dimensions
• Bulk Fields and Supersymmetry in a Slice of AdS
• Is the Lightest Kaluza-Klein Particle a Viable Dark Matter Candidate?
• Kaluza-Klein Dark Matter
• Bulk Gauge Fields in the Randall-Sundrum Model
• Gauge bosons in a five-dimensional theory with localized gravity
• Dark Matter and Collider Phenomenology of Universal Extra Dimensions
• Bosonic Supersymmetry? Getting Fooled at the LHC
• Bulk Standard Model in the Randall-Sundrum Background
• On the Unification Problem in Physics
• Elastic Scattering and Direct Detection of Kaluza-Klein Dark Matter
• Search for resonant and nonresonant new phenomena in high-mass dilepton final states at $\sqrt{s}=$ 13 TeV
• Search for new phenomena in events with an energetic jet and missing transverse momentum in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Precise Calculation of the Relic Density of Kaluza-Klein Dark Matter in Universal Extra Dimensions
• Probing Kaluza-Klein Dark Matter with Neutrino Telescopes
• Dark matter in UED : the role of the second KK level
• Spinless photon dark matter from two universal extra dimensions
• Search for physics beyond the standard model in high-mass diphoton events from proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Search for heavy particles decaying into a top-quark pair in the fully hadronic final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Current LHC Constraints on Minimal Universal Extra Dimensions
• Discriminating dark matter candidates using direct detection
• LHC Collider Phenomenology of Minimal Universal Extra Dimensions
• Monoenergetic Gamma-Rays from Non-Minimal Kaluza-Klein Dark Matter Annihilations
• Hidden symmetries induced by a canonical transformation and gauge structure of compactified Yang-Mills theories
• Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics
• Yang-Mills theories with an arbitrary number of compactified extra dimensions
• Distinctive ultraviolet structure of extra-dimensional Yang-Mills theories by integration of heavy Kaluza-Klein modes
• Effects of universal extra dimensions on top-quark electromagnetic interactions
• Gauge-invariant approach to the beta function in Yang-Mills theories with universal extra dimensions
• Gauge invariance and radiative corrections in an extra dimensional theory

Cited by in corpus (1)

• Gauge-invariant approach to the beta function in Yang-Mills theories with universal extra dimensions