Localization mechanism of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi></mml:math>-form field on the braneworld by coupling with gravity

It is known that the scalar fields can be trapped on branes of different types, and the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:math> gauge vector fields can be localized on the thick de Sitter brane, or the thick Minkowski brane via coupling with gravity. The Kalb-Ramond fields can be localized on the Minkowski brane and the thick de-Sitter brane, with certain couplings. In this paper, with considering a coupling mechanism between the kinetic term of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>q</e:mi></e:math>-form fields and the background spacetime, we investigate the localization of Kaluza-Klein modes for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>q</g:mi></g:math>-form fields in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>D</i:mi></i:math>-dimensional spacetime. Concrete <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>q</k:mi></k:math>-form fields are discussed within five-dimensional brane models with typical spacetime geometries: Minkowski, de Sitter, and anti–de Sitter. In the Minkowski brane case, the zero modes of various <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>q</m:mi></m:math>-form fields can be localized on the brane. In the de Sitter brane case, the zero mode of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>U</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1</o:mn><o:mo stretchy="false">)</o:mo></o:math> gauge vector fields can be localized on the brane. Lastly in the anti–de Sitter brane case, the zero mode of the Kalb-Ramond fields can be localized on the brane. For the massive Kaluza-Klein modes of these <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>q</s:mi></s:math>-form fields, they could be localized or quasi-localized on the brane of different types. Besides, subtle and detailed behaviors of the Kaluza-Klein modes for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>q</u:mi></u:math>-form fields are observed: the zero modes could be localized on both sides of the brane, and the massive modes could be localized or quasilocalized at the brane position.