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Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of ascale invariant theory which does not possess conformal symmetry -- the specialconformal transformation(SCT) explicitly breaks the gauge invariance of thetheory. In this work, we construct a non-local gauge-invariant extension of theSCT, which is compatible with the BRST formalism and defines a new symmetry ofthe physical Hilbert space of the Maxwell theory for any dimension $d\geqslant3$. We prove the invariance of the Maxwell theory in $d\geqslant 3$ byexplicitly showing that the gauge-invariant two-point correlation functions,the action, and the classical equation of motion are unchanged under such atransformation.

Extended Conformal Symmetry in $d\neq 4$: Conformal Symmetry of Abelian Gauge Theory in the Physical Sector