In string theory textbooks we learn that there are two types of supersymmetric heterotic strings, namely E8 x E8 and Spin(32)/Z_2 . Are we sure that they are the only ones? The textbooks also explain that there are some non-supersymmetric heterotic strings obtained by alternative GSO projections. Are we sure that we already found all such non-supersymmetric heterotic strings? Finally, we don't usually talk about branes in heterotic strings except for NS5-branes. Are we sure there aren't others? In this talk I'd like to answer these questions, using modern but basic techniques on 2d CFT. (Spoiler alert: the answers are yes, yes and no.) The talk is based on a number of long-running projects with many friends: Philip Boyle Smith, Justin Kaidi, Ying-Hsuan Lin, Kantaro Ohmori, Vivek Saxena, Mayuko Yamashita, Kazuya Yonekura, and Yunqin Zheng.
Introduction: Prof. Yuji Tachikawa is currently a professor at Kavli IPMU, Tokyo University. He works on mathematical aspects of string theory and quantum field theory. He received the New Horizons in Physics Prize in 2016.
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Prof. Yinan Wang