Wall crossing, discrete attractor flow and Borcherds algebra
Wall crossing, discrete attractor flow and Borcherds algebra
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穿墙、离散吸引子流和 Borcherds 代数
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
E. Verlinde
中科院分区：
文献类型：
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作者：
Miranda C.N. Cheng;E. Verlinde
阐明了 N=4、d=4 弦理论中 BPS dyon 谱中广义（或 Borcherds-）Kac-Moody 代数的出现。通过低能超重力分析，我们将其根晶格确定为双子电荷T-对偶不变量的晶格，根系的对称群为理论的扩展S-对偶群PGL(2,Z)，Weyl室壁为相关双心解的边际稳定壁。这导致将 Weyl 群解释为穿壁群或离散吸引子流群。此外，我们提出了电荷和模数相关的最高权重向量的“第二量子化多重性”与动力简并性之间的等价性，并表明根据我们的建议得出的穿墙公式与从超重力分析中获得的穿墙公式一致。这可以被认为是提供了该理论的穿墙公式的微观推导。
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a 'second-quantized multiplicity' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory.