Orientifold Donaldson-Thomas theory of quivers

Abstract

Motivated by the counting of BPS states in string theory with orientifolds, we study moduli spaces of self-dual representations of a quiver with contravariant involution. Wall-crossing formulas, describing the behaviour of generating functions counting semistable self-dual representations under changes in stability, recover formulas predicted in the string theory literature on orientifolds. In certain cases, wall-crossing can be understood in terms of quantum dilogarithm identities that are in some sense square roots of the identities appearing in ordinary Donaldson-Thomas theory. The main tool we use is a representation of the Hall algebra that is of independent interest- it is a model for the space of BPS states in an orientifolded theory.