arXiv 1908.071772019-08-20hep-th

立方弦场论中的Bernoulli数与多重膜解

Bernoulli Numbers and Multi-brane Solutions in Cubic String Field Theory

Hiroyuki Hata

备注：: 21 pages, no figures

摘要：

在以前的论文[arXiv：1901.01681]中，我们给出了立方开弦场论（CSFT）中任意整数膜数的多膜解的解析构造。我们的$(N+1)$膜解以纯规范形式$Ψ=U Q_\textrm{B}U^{-1}$给出，它是关于由$[N/2]$独立实参数$α_k$指定的酉弦场$U$的.我们看到，对于$N$ $(=2, 3, 4, 5,\cdots)$的不同样本值，$α_k$可以一致地由两个要求确定：作用的能量密度应该重现$(N+1)$ -膜的能量密度，解对解本身的EOM应该成立。在本文中，我们完成了我们的建设，确定$α_k$满足两个通用$N$的要求。我们发现，每个$α_k$是在一个封闭的形式，通过使用伯努利数。我们还提出了一些补充结果，我们的解决方案，从它的引力耦合，和酉弦场$U$作为一个指数函数的能量密度的解决方案。

英文摘要：

In a previous paper [arXiv:1901.01681], we presented an analytic construction of multi-brane solutions in cubic open string field theory (CSFT) for any integer brane number. Our $(N+1)$-brane solution is given in the pure-gauge form $Ψ=U Q_\textrm{B}U^{-1}$ in terms of a unitary string field $U$ which is specified by $[N/2]$ independent real parameters $α_k$. We saw that, for various sample values of $N$ $(=2, 3, 4, 5,\cdots)$, $α_k$ can be consistently determined by two requirements: The energy density from the action should reproduce that of $(N+1)$-branes, and the EOM of the solution against the solution itself should hold. In this paper, we complete our construction by determining $α_k$ satisfying the two requirements for a generic $N$. We find that each $α_k$ is given in a closed form by using the Bernoulli numbers. We also present some supplementary results on our solution; the energy density of the solutions determined from its gravitational coupling, and the unitary string field $U$ as an exponential function.

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摘要：

英文摘要：

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