The planar phase of superfluid ³He has Dirac points in momentum space and the analog of Dirac monopole in the real space. Here we discuss the combined effect of Dirac point and Dirac monopole. It is shown that in the presence of the monopole the effective metric acting on Dirac fermions corresponds to the metric produced by the global monopole in general relativity: it is the conical metric. Another consequence is that the primary variable, which gives rise to the effective metric, is the unusual vielbein field in the form of the 4 × 5 matrix, as distinct from the conventional 4 × 4 matrix of the tetrad field in tetrad gravity.

中文翻译：

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Vielbein具有3维超流3 He平面相中的混合维数和引力全局单极子

超流体³ He的平面相位在动量空间中具有狄拉克点，在实际空间中具有狄拉克单极子的类似物。在这里，我们讨论狄拉克点和狄拉克单极子的组合效应。结果表明，在存在单极子的情况下，作用于狄拉克费米子的有效度量对应于广义相对论中整体单极所产生的度量：它是圆锥形度量。另一个结果是，引起有效度量的主要变量是4×5矩阵形式的不寻常的vielbein场，这与传统的4d场的4d矩阵在4d重力下不同。