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The definitions of the nth Gauss sum and the associated nth central charge are introduced for premodular categories C and n∈ Z. We first derive an expression of the nth Gauss sum of a modular category C, for any integer n coprime to the order of the T-matrix of C, in terms of the first Gauss sum, the global dimension, the twist and their Galois conjugates. As a consequence, we show for these n, the higher Gauss sums are d-numbers and the associated central charges are roots of unity. In particular, if C is the Drinfeld center of a spherical fusion category, then these higher central charges are 1. We obtain another expression of higher Gauss sums for de-equivariantization and local module constructions of appropriate premodular and modular categories. These expressions are then applied to prove the Witt invariance of higher central charges for pseudounitary modular categories.

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Selecta Mathematica, New Series