论文标题
D4-D2-D0索引的模块化引导程序三倍
Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds
论文作者
论文摘要
我们调查了BPS指数的生成系列$ H_R（τ）$的模块化约束，计算D4-D2-D0绑定状态的固定D4-Brane Charge $ r $ r $ in Type IIA字符串理论在完整交叉点Calabi-yau三倍的$ b_2 = 1 $中calabi-yau三倍。对于D4-Brane单元，$ h_1 $在$ sl（2，z）$的动作下以（矢量值）模块化形式转换为（矢量值），因此完全由其极性项决定。我们根据排名1 Donaldson-Thomas不变式为这些术语提出了一个ANSATZ，其中包含了单个D6-ANTI-D6对的贡献。 Using an explicit overcomplete basis of the relevant space of weakly holomorphic modular forms (valid for any $r$), we find that for 10 of the 13 allowed threefolds, the Ansatz leads to a solution for $h_1$ with integer Fourier coefficients, thereby predicting an infinite series of DT invariants.For $r > 1$, $h_r$ is mock modular and determined by its polar part together with its 阴影。仅限于$ r = 2 $，我们使用一系列Hurwitz类数字来构建一个$ h^{an} _2 $，与$ H_2 $完全相同的模块化异常，以便差异$ h_ {2} -h^{an} _2 _2 _2 _2 _2 _2 $是固定的普通模块形式。由于缺乏令人满意的Ansatz，我们将这些极性术语的确定作为一个开放的问题。
We investigate the modularity constraints on the generating series $h_r(τ)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane charge $r$ in type IIA string theory compactified on complete intersection Calabi-Yau threefolds with $b_2 = 1$. For unit D4-brane, $h_1$ transforms as a (vector-valued) modular form under the action of $SL(2,Z)$ and thus is completely determined by its polar terms. We propose an Ansatz for these terms in terms of rank 1 Donaldson-Thomas invariants, which incorporates contributions from a single D6-anti-D6 pair. Using an explicit overcomplete basis of the relevant space of weakly holomorphic modular forms (valid for any $r$), we find that for 10 of the 13 allowed threefolds, the Ansatz leads to a solution for $h_1$ with integer Fourier coefficients, thereby predicting an infinite series of DT invariants.For $r > 1$, $h_r$ is mock modular and determined by its polar part together with its shadow. Restricting to $r = 2$, we use the generating series of Hurwitz class numbers to construct a series $h^{an}_2$ with exactly the same modular anomaly as $h_2$, so that the difference $h_{2}-h^{an}_2$ is an ordinary modular form fixed by its polar terms. For lack of a satisfactory Ansatz, we leave the determination of these polar terms as an open problem.
