Geometric engineering of (framed) BPS states
Geometric engineering of (framed) BPS states
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DOI：
10.4310/atmp.2014.v18.n5.a3
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发表时间：
2013-01
影响因子：
1.5
通讯作者：
Wu-yen Chuang;D. Diaconescu;J. Manschot;G. Moore;Y. Soibelman
中科院分区：
文献类型：
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作者：
Wu-yen Chuang;D. Diaconescu;J. Manschot;G. Moore;Y. Soibelman
通过几何工程从复曲面卡-丘三重范畴导出了$\mathcal{N} = 2 \：SU（N）$规范理论的BPS箭图。虽然结果是在以前的低能量建设的协议，几何方法导致几个新的结果。一个没有墙猜想制定的所有值的$N$，有关的场论BPS光谱大半径D-膜束缚态。支持的证据作为显式计算的BPS简并在一些例子中。这些计算也证明了在弱耦合下存在任意高自旋和无穷多个边缘稳定壁的BPS态。此外，框架BPS状态的框架BPS模型自然来自这种形式主义，以及在motivic和上同调Donaldson-Thomas不变量方面的框架和非框架BPS简并的数学公式。我们用动力学DT不变量验证了具有奇异SU（2）R量子数的BPS态的不存在.这个应用程序是特别是基于一个完整的递归算法，它确定了非框架的BPS频谱在任何一点上的库仑分支的非交换唐纳森-托马斯不变量为框架的BPS表示。
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.