Open Access
October 2014 Geometric engineering of (framed) BPS states
Wu-yen Chuang, Duiliu-Emanuel Diaconescu, Jan Manschot, Gregory W. Moore, Yan Soibelman
Adv. Theor. Math. Phys. 18(5): 1063-1231 (October 2014).


BPS quivers for $\mathcal{N} = 2 \: SU(N)$ gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous low energy constructions, the geometric approach leads to several new results. An absence of walls conjecture is formulated for all values of $N$, relating the field theory BPS spectrum to large radius D-brane bound states. Supporting evidence is presented as explicit computations of BPS degeneracies in some examples. These computations also prove the existence of BPS states of arbitrarily high spin and infinitely many marginal stability walls at weak coupling. Moreover, framed quiver models for framed BPS states are naturally derived from this formalism, as well as a mathematical formulation of framed and unframed BPS degeneracies in terms of motivic and cohomological Donaldson-Thomas invariants. We verify the conjectured absence of BPS states with "exotic" $SU(2)_R$ quantum numbers using motivic DT invariants. This application is based in particular on a complete recursive algorithm which determines the unframed BPS spectrum at any point on the Coulomb branch in terms of noncommutative Donaldson-Thomas invariants for framed quiver representations.


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Wu-yen Chuang. Duiliu-Emanuel Diaconescu. Jan Manschot. Gregory W. Moore. Yan Soibelman. "Geometric engineering of (framed) BPS states." Adv. Theor. Math. Phys. 18 (5) 1063 - 1231, October 2014.


Published: October 2014
First available in Project Euclid: 25 November 2014

zbMATH: 1365.81092
MathSciNet: MR3281276

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 5 • October 2014
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