▁both ▁sides ▁of ▁the ▁du ality , ▁and ▁they ▁agree ▁as ▁they ▁must ▁in ▁accord ance ▁with ▁Ger ard ▁' t ▁H oo ft ' s ▁anom aly ▁matching ▁conditions . ▁The ▁role ▁of ▁the ▁additional ▁fundamental ▁mes on ▁super field ▁M ▁in ▁the ▁dual ▁theory ▁is ▁very ▁cru cial ▁in ▁matching ▁the ▁anom al ies . ▁The ▁global ▁gravit ational ▁anom al ies ▁also ▁match ▁up ▁as ▁the ▁par ity ▁of ▁the ▁number ▁of ▁ch iral ▁fields ▁is ▁the ▁same ▁in ▁both ▁theories . ▁The ▁R - charge ▁of ▁the ▁W ey l ▁ferm ion ▁in ▁a ▁ch iral ▁super field ▁is ▁one ▁less ▁than ▁the ▁R - charge ▁of ▁the ▁super field . ▁The ▁R - charge ▁of ▁a ▁g aug ino ▁is ▁+ 1 . ▁ ▁Another ▁evidence ▁for ▁Se i berg ▁du ality ▁comes ▁from ▁ident ifying ▁the ▁super con form al ▁index , ▁which ▁is ▁a ▁general ization ▁of ▁the ▁W itten ▁index , ▁for ▁the ▁electric ▁and ▁the ▁magnetic ▁phase . ▁The ▁identification ▁gives ▁rise ▁to ▁complicated ▁integral ▁ident ities ▁which ▁have ▁been ▁studied ▁in ▁the ▁mathematical ▁literature . ▁ ▁General izations ▁ ▁Se i berg ▁du ality ▁has ▁been ▁generalized ▁in ▁many ▁directions . ▁ ▁One ▁general ization ▁applies ▁to ▁qui ver ▁gauge ▁theories , ▁in ▁which ▁the ▁flav or ▁symmet ries ▁are ▁also ▁g aug ed . ▁ ▁The ▁simplest ▁of ▁these ▁is ▁a ▁super ▁Q CD ▁with ▁the ▁flav or ▁group ▁g aug ed ▁and ▁an ▁additional ▁term ▁in ▁the ▁super pot ential .