# Tagged Questions

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### relating spinor and fundamental representation for $E_8$

While proving a very important relation which is satisfied both by $SO(32)$ AND $E_8$, which makes it possible to factorize the anomaly into two parts. The relation is ...
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### Traces in different representation

I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
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### What is 'heterotic string compactification'?

I've read that some exceptional groups arises in the context of 'heterotic string compactification'. Could someone explain (to a person studying physics but who doesn't know string theory) what ...
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### Spinor representation restricted under subgroup, a formula from Polchinski

The question is about the spinor representation decomposed under subgroups. It's a common technique in string theory when parts of dimensions are compactified and ignored, and we are only interested ...
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### Decomposition of Representation Multiplication

How can the multiplication of spinor representations (of $SO(8)$) $8_+ \otimes 8_-$ be decomposed into $8_v \oplus 56_v$? Where can I read more about the decomposition rule of different ...
I am going through Tong's lecture notes on String Theory and came across the following irrep decomposition (Chap 2, p.43) of the bosonic string first excited states: $$\text{traceless symmetric} ... 1answer 343 views ### Vector and Spinor Representation in Ramond-Neveu-Schwarz Superstring Theory I am learning Ramnond-Neveu-Schwarz Superstring theory (RNS theory). I often find the following notation, especially in the closed string spectrum etc.:$$\mathbf{8}_s,\mathbf{8}_v  And it is ...
In Green-Schwarz-Witten Volume 2, chapter 15, it is argued (roughly) that we need 6-dimensional manifolds of $SU(3)$ holonomy in order to receive 1 covariantly constant spinor field. And it turns out ...