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arXiv 2207.01474hep-th
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关于伽利略共形引导程序II：$ξ=0$扇区

On Galilean Conformal Bootstrap II: $ξ=0$ sector

Bin Chen, Peng-xiang Hao, Reiko Liu, Zhe-fei Yu

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摘要：

在这篇文章中，我们继续了我们在二维伽利略共形场论（GCFT $_2$）上的工作。我们之前的工作（arXiv：2011.11092）主要关注$ξ\neq 0$扇区，在这里我们研究更微妙的$ξ=0$扇区以完成讨论。$ξ=0$是简并的，因为在一般的$ξ=0$增强多重态中出现了有趣的零态。我们指定这些空状态，并制定出相应的选择规则。然后，我们计算$ξ=0$全局GCA块，发现它们可以被写为几个构建块的线性组合，每个构建块可以从$sl(2,\mathbb{R})$ Casimir方程获得。这些积木也允许我们给出一个欧几里得反演公式。作为一致性检验，我们研究了BMS自由标量理论中某些顶点算子的四点函数。在这种情况下，$ξ=0$扇区是传播信道中唯一允许的扇区。我们发现四点函数的直接展开再现了全局GCA块，并且与反演公式一致。

英文摘要：

In this work, we continue our work on two dimensional Galilean conformal field theory (GCFT$_2$). Our previous work (arXiv:2011.11092) focused on the $ξ\neq 0$ sector, here we investigate the more subtle $ξ=0$ sector to complete the discussion. The case $ξ=0$ is degenerate since there emerge interesting null states in a general $ξ=0$ boost multiplet. We specify these null states and work out the resulting selection rules. Then, we compute the $ξ=0$ global GCA blocks and find that they can be written as a linear combination of several building blocks, each of which can be obtained from a $sl(2,\mathbb{R})$ Casimir equation. These building blocks allow us to give an Euclidean inversion formula as well. As a consistency check, we study four-point functions of certain vertex operators in the BMS free scalar theory. In this case, the $ξ=0$ sector is the only allowable sector in the propagating channel. We find that the direct expansion of the 4-point function reproduces the global GCA block and is consistent with the inversion formula.

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