We explore unified field theories based on the gauge groups $SU(5)$ and $SO(10)$ using the worldline approach for chiral fermions with a Wilson loop coupling to a background gauge field. Representing path ordering and chiral projection operators with functional integrals has previously reproduced the sum over the chiralities and representations of standard model particles in a compact way. This paper shows that for $SU(5)$ the $\bar{\mathbf{5}}$ and $\mathbf{10}$ representations -- into which the Georgi-Glashow model places the left-handed fermionic content of the standard model -- appear naturally and with the familiar chirality. We carry out the same analysis for flipped $SU(5)$ and uncover a link to $SO(10)$ unified theory. We pursue this by exploring the $SO(10)$ theory in the same framework, the less established unified theory based on $SU(6)$ and briefly consider the Pati-Salam model using $SU(4) \!\times \!SU(2)\! \times\! SU(2)$.
Chiral symmetry: An analytic $SU(3) $ unitary matrix
在强子低能过程中使用的$SU(2)$酉矩阵$U$既有指数表示又有解析表示，与之相关的是$ U = \exp\left[ i \mathbfτ \cdot \hat{\mathbfπ} θ\,\right] = \cosθI + i \mathbfτ \cdot \hat{\mathbfπ} \sinθ$。通过导出解析表达式将该结果扩展到$SU(3)$酉矩阵，对于盖尔曼矩阵$\mathbfλ$，该解析表达式读作$ U= \exp\left[ i \mathbf{v} \cdot \mathbfλ \right] = \left[ \left( F + \tfrac{2}{3} G \right) I + \left( H \hat{\mathbf{v}} + \tfrac{1}{\sqrt{3}} G \hat{\mathbf{b}} \right) \cdot \mathbfλ \, \right] + i \left[ \left( Y + \tfrac{2}{3} Z \right) I + \left( X \hat{\mathbf{v}} + \tfrac{1}{\sqrt{3}} Z \hat{\mathbf{b}} \right) \cdot \mathbfλ \right] $，其中$v_i=[\,v_1, \cdots v_8\,]$、$ b_i = d_{ijk}…
On Supersymmetric D-brane probes in 4d $\mathcal{N}=2$ $\text{AdS}_2\times\mathbf{S}^2$ Attractors
Enrico Fermi Institute & Leinweber Institute for Theoretical Physics, University of Chicago（恩里科·费米研究所与莱因韦伯理论物理研究所，芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（卡弗里宇宙物理学研究所，芝加哥大学）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理学研究所（维尔纳·海森堡研究所））
Worldsheet string theory on $\mathrm{AdS}_3 \times \mathbf{S}^3 \times \mathrm{K3}$
University of the Chinese Academy of Sciences（中国科学院大学）；Institute for Theoretical Physics, University of Amsterdam（阿姆斯特丹大学理论物理研究所）；Institut für Theoretische Physik, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Department of Mathematics, King’s College London（伦敦国王学院数学系）；Center for Quantum Mathematics and Physics (QMAP) Department of Physics & Astronomy, University of California, Davis（加州大学戴维斯分校物理学与天文学系量子数学与物理中心）
Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain
