<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:math> symmetry and its breaking in the chiral fermion formalism

In this paper, we review the fundamental aspects of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:math> supergravity and employ the chiral formalism to describe spin-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mfrac><d:mn>3</d:mn><d:mn>2</d:mn></d:mfrac></d:math> fermions. Armed with this, we analyze the discrete symmetries of the graviton in the context of linearized gravity (LG) and Rarita-Schwinger (RS) fields, which include the description of the gravitino. Additionally, we highlight the advantages of the chiral formalism in classifying Lorentz and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>C</f:mi><f:mi>P</f:mi><f:mi>T</f:mi></f:math>-violating terms in RS theories, extending these models by including Lorentz-violating operators, as has been done in LG.