A comment on the χy genus and supersymmetric quantum mechanics

In this Letter we show that a simple modification of supersymmetric quantum mechanics involving a mass term for half the fermions naturally leads to a derivation of the integral formula for the χy genus, a quantity that interpolates between the Euler characteristic and arithmetic genus. We note that this modification naturally arises in the moduli space dynamics of monopoles or instantons in theories with 16 supercharges partially broken to 8 supercharges by mass terms.