Abstract
Free massless scalars have a shift symmetry. This is usually broken by gauge and Yukawa interactions, such that quantum corrections induce a quadratically divergent mass term. In the Standard Model this leads to the hierarchy problem of the electroweak theory, the question why the Higgs mass is so much smaller than the Planck mass. We present an example where a large scalar mass term is avoided by coupling the scalar to an infinite tower of massive states which are obtained from a six-dimensional theory compactified on a torus with magnetic flux. The series of divergent quantum corrections adds up to zero, and we show explicitly that the shift symmetry of the scalar is preserved in the effective four-dimensional theory despite the presence of gauge and Yukawa interaction terms.
Highlights
JHEP08(2018)151 illustrates how such a shift symmetry can arise in compactifications with magnetic flux, and we shall identify the higher-dimensional origin of the symmetry
We present an example where a large scalar mass term is avoided by coupling the scalar to an infinite tower of massive states which are obtained from a six-dimensional theory compactified on a torus with magnetic flux
The series of divergent quantum corrections adds up to zero, and we show explicitly that the shift symmetry of the scalar is preserved in the effective four-dimensional theory despite the presence of gauge and Yukawa interaction terms
Summary
Let us consider a left-handed 6d Weyl fermion interacting with an Abelian gauge field,. In order to obtain the effective 4d action one expands the 6d fields into mode functions corresponding to eigenstates of the kinetic term of the compact dimensions. For charged fields these are Landau levels obtained from an harmonic oscillator algebra [5, 15, 27]. The effective action (2.26) is very different from the 4d action without magnetic flux In this case one obtains a vector-like theory, and after spontaneous symmetry breaking the lowest states of the spectrum consist of a Dirac fermion, a real scalar and a vector, which all have masses of the order of the compactification scale. Contrary to the case of the Standard Model, its vacuum expectation value does not give mass to the chiral fermions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
