论文标题
在Galilean Constromal Bootstrap II：$ξ= 0 $ sector
On Galilean Conformal Bootstrap II: $ξ=0$ sector
论文作者
论文摘要
在这项工作中，我们继续在二维Galilean共形场理论（GCFT $ _2 $）上进行工作。我们以前的工作（Arxiv：2011.11092）着重于$ξ\ neq 0 $ sector，在这里我们调查了更微妙的$ξ= 0 $ sector，以完成讨论。情况$ξ= 0 $是退化的，因为在一般$ξ= 0 $ boost倍增中出现了有趣的空状态。我们指定这些无效状态并制定结果选择规则。然后，我们计算$ξ= 0 $全局GCA块，发现它们可以写成几个构建块的线性组合，每个块可以从$ sl（2，\ mathbb {r}）$ casimir方程中获得。这些构建块使我们也可以给出欧几里得反转公式。作为一致性检查，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 $ sector是传播通道中唯一的允许扇区。我们发现4点函数的直接扩展会重现全局GCA块，并且与反转公式一致。
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.
