Localization of gravitino field on f(R, Q, P) brane

Abstract In this paper we consider the localization of the gravitino field on a codimension-one thick brane within the framework of f ( R , Q , P ) gravity. First, setting $$F(\phi ) = \phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:math> , we derive the potential functions for various parameters. Under appropriate coupling parameters, we can find the localized zero mode and some resonance states. Furthermore, we use these resonance states as initial data to investigate the evolution of the gravitino resonances. It can be observed that various parameters on the brane affect the evolution duration. We focus on comparing the localization behavior of the gravitino field on the brane for the cases with $$k=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and $$k\ne 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> .