Communications in Number Theory and Physics

Volume 9 (2015)

Number 3

Self-dual quiver moduli and orientifold Donaldson-Thomas invariants

Pages: 437 – 475



Matthew B. Young (Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong)


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.We develop Hall module techniques to compute the number of points over finite fields of moduli stacks of semistable self-dual representations. Wall-crossing formulas relating these counts for different choices of stability parameters recover the wall-crossing of orientifold BPS/Donaldson-Thomas invariants predicted in the physics literature. In finite type examples the wall-crossing formulas can be reformulated in terms of identities for quantum dilogarithms acting on representations of quantum tori.

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