Wall Crossing and M-Theory

Abstract

We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a CalabiYau 3-fold X. When X has no compact 4-cycles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kähler moduli space.2010 Mathematics Subject Classification: 14N35. Keywords: string theory, bound state, Fock space, Calabi-Yau manifold. §1. IntroductionThe topological string theory gives solutions to a variety of counting problems in string theory and M-theory. From the worldsheet perspective, the A-model topological string partition function Z top generates the Gromov-Witten invariants, which count holomorphic curves in a Calabi-Yau (CY) 3-fold X. On the other hand, from the target space perspective, Z top computes the Gopakumar-Vafa (GV) invariants, which count BPS states of spinning black holes in 5 dimensions constructed from M2 branes in M-theory on X [9]. Moreover, the absolute-valueThis is a contribution to the special issue "The golden jubilee of algebraic analysis".Communicated by M. Kashiwara.

BPS states, knots, and quivers

“…Second, colored HOMFLY-PT polynomials and LMOV invariants are naturally defined for arbitrary representations, while for symmetric representations they are related to algebraic curves of A-polynomial type, as well as recursion relations encoded in polynomials [11,12,35]. We expect that analogous objects should exist for quivers, presumably generalizing observations in [18].…”

Refined open noncommutative Donaldson–Thomas invariants for small crepant resolutions

“…• See [Jafferis and Moore 2008;Chuang and Jafferis 2009;Aganagic et al 2011;Chuang and Pan 2010;Aganagic and Yamazaki 2010;Dimofte et al 2011] for developments in physics.…”

Dual little strings and their partition functions

“…If we place Lagrangian branes [44] on (pairs of) external legs of the web diagram, the curves contributing to the open string amplitude (4.7) are of type (i) if the external legs are on different sides of the diagram and of type (ii) if they are on the same side, respectively. In the former case, for two external legs labeled by α i and β j , these curves are shown in Fig.…”