KDD[i, j] is the Kronecker delta in D-1 dimensions.
KDD[i, j]\delta ^{ij}
Contract[KDD[i, j] KDD[i, j]]D-1
KDD[a, b] // StandardForm
(*KDD[a, b]*)FCI[KDD[a, b]] // StandardForm
(*CartesianPair[CartesianIndex[a, -1 + D], CartesianIndex[b, -1 + D]]*)FCE[FCI[KDD[a, b]]] // StandardForm
(*KDD[a, b]*)