| Summary: | This paper investigates gauge invariance in a bulk massless q-form field on a p-brane with codimension two, utilizing a general Kaluza–Klein (KK) decomposition. The KK decomposition analysis reveals four distinct KK modes: the conventional <i>q</i>-form, two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-forms and one <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-form. These diverse modes are essential for maintaining gauge invariance. We also find eight Schrödinger-like equations for the four modes due to the two extra dimensions, and their mass spectra are closely related. The KK decomposition process gives rise to four dualities on the p-brane, originating from the inherent Hodge duality present in the bulk. Notably, these dual symmetries play a significant role in maintaining the equivalence of bulk dual fields during dimensional reduction.
|
|---|