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An abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet allows for a dualitytransformation to be applied to one of its spin-0 states. The resulting theorycan be described as an abelian 4D, $\mathcal{N}$ = 4 vector-tensorsupermultiplet. It is seen to decompose into a direct sum of an off-shell 4D,$\mathcal{N}$ = 2 vector supermultiplet and an off-shell 4D, $\mathcal{N}$ = 2tensor supermultiplet. The commutator algebra of the other two supersymmetriesare still found to be on-shell. However, the central charge structure in theresulting 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet is considerablysimpler that that of the parent abelian 4D, $\mathcal{N}$ = 4 vectorsupermultiplet. This appears to be due to the replacement of the usual SO(4)symmetry associated with the abelian 4D, $\mathcal{N}$ = 4 vectorsupermultiplet being replaced by aGL(2,$\mathbb{R}$)$\otimes$GL(2,$\mathbb{R}$) symmetry in the 4D, $\mathcal{N}$= 4 vector-tensor supermultiplet. The $Mathematica$ code detailing thecalculations is available open-source at the HEPTHools Data Repository onGitHub.

Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure