Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers

Abstract: We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras.