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arXiv 2109.02003hep-th
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开弦场论中 $a$-规范下的数值普适解

Numerical universal solutions in $a$-gauge in open string field theory

Isao Kishimoto

备注：
28 pages, 16 figures; v2: a reference added
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AI总结：

本文在玻色开弦场论中利用能级截断和连续形变构造 $a$-规范数值普适解，发现“双膜”解的规范不变量随 $a$ 显著变化，并可能在 $0.5<a<1$ 时转变为单膜解。

摘要：

在玻色开弦场论中，除快子真空解外，我们还构造了 $a$-规范下与 Siegel 规范中“双膜”解和“鬼膜”解相对应的数值普适解，并计算了它们的规范不变量，即能量和规范不变可观测量。$a$-规范条件包含一个实参数 $a$，由 Asano 和 Kato 引入。在早期工作中，它已被用于通过能级截断法寻找最高至能级 14 的快子真空解。“双膜”和“鬼膜”解由 Kudrna 和 Schnabl 在对应于（$a=0$）规范的 Siegel 规范中构造，最高至能级 28。从这些解出发，通过逐步小幅改变 $a$，我们在包括 $a=\infty$ 在内的各种 $a$ 值下构造了最高至能级 20 的 $a$-规范数值解。与朴素预期相反，$a$-规范下“双膜”和“鬼膜”解的规范不变量似乎并不随 $a$ 保持恒定。特别地，尽管 $a$-规范下“双膜”解的归一化能量 $E$ 在 $a\sim0$ 时约为 2，但我们发现，在 $0.5<a<1$ 时 $E$ 几乎变为 1。规范不变可观测量也表现出类似行为。这或许意味着，在此类 $a$-规范中，“双膜”解会转变为单膜解。

英文摘要：

In bosonic open string field theory, we construct numerical universal solutions in $a$-gauge corresponding to ``double brane'' and ``ghost brane'' solutions in Siegel gauge in addition to the tachyon vacuum solution, and evaluate their gauge invariants, which are energy and gauge-invariant observable. The $a$-gauge condition, which contains a real parameter $a$, was introduced by Asano and Kato. In earlier works it has been applied to find the tachyon vacuum solution with the level truncation method up to level $14$. The ``double brane'' and ``ghost brane'' solutions were constructed by Kudrna and Schnabl in Siegel gauge, which corresponds to ($a=0$)-gauge, up to level $28$. Starting from these solutions, by varying $a$ little by little, we have constructed numerical solutions in $a$-gauge for various values of $a$ including $a=\infty$ up to level $20$. Contrary to naive expectation, the gauge invariants of ``double brane'' and ``ghost brane'' solutions in $a$-gauge seem to be non-constant for $a$. In particular, although the normalized energy $E$ of the ``double brane'' solution in $a$-gauge is approximately two for $a\sim 0$, we find that $E$ becomes almost one for $0.5<a<1$. The gauge-invariant observable also behaves similarly. It might imply that the ``double brane'' solution varies to a single brane solution in such $a$-gauges.

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