Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories

Abstract

We consider a topological coupling between a pseudo-scalar field and a 3-form gauge field in $\mathcal{N}=1$ supersymmetric higher derivative 3-form gauge theories in four spacetime dimensions. We show that ghost/tachyon-free higher derivative Lagrangians with the topological coupling can generate various potentials for the pseudo-scalar field by solving the equation of motion for the 3-form gauge field. We give two examples of higher derivative Lagrangians and the corresponding potentials: one is a quartic order term of the field strength and the other is the term which can generate a cosine-type potential of the pseudo-scalar field.

v1: 30 pages; v2: 32 pages, 2 figures, references added, published version

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