Understanding SO(10) GUT Representations

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In summary, the conversation discusses learning about GUTs, specifically SO(10) models and their representations. The \overline{16} representation is mentioned as coupling Higgs fields to particles. The difference between a 126 and \overline{126} representation is questioned and reference suggestions are given. It is noted that Sash126bar is the complex conjugate of the 126 representation and recommendations for further reading are made.
  • #1
Saschenka
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Hi, all!

I am about to learn how GUTs (specifically SO(10)) work, but I am stuck already at the different representations.

In SO(10) models all particles are in a [itex]\overline{16}[/itex].
Since [itex]\overline{16}[/itex] x [itex]\overline{16}[/itex] = 10 + [itex]\overline{126}[/itex] + 120, one can couple Higgs fields transforming as 10, [itex]\overline{126}[/itex], or 120 to the particles.

My first question would be: What's the difference between a 126 and a [itex]\overline{126}[/itex]?

Maybe someone has a good reference to learn this stuff. I am reading "Grand Unified Theories" from Graham G. Ross currently, but there the above question is not answered. Maybe it's too basic... In scientific papers usually nothing at all is explained (from my perspective...).

Thanks a lot for your help!

Sash
 
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  • #2
126bar is the complex conjugate of the 126 representation.
 
  • #3
Try Georgi. Still one of the best texts to read about unification (and Lie algebras in fundamental physics in general). Also, Zee's QFT book has some nice sections about it. :)
 

1. What is SO(10) GUT?

SO(10) GUT stands for Special Orthogonal Group with rank 10 Grand Unified Theory. It is a theoretical framework in particle physics that aims to unify the three fundamental forces of nature (electromagnetism, strong nuclear force, and weak nuclear force) into a single force. It also predicts the existence of a new type of particle called a "gauge boson" that mediates the unified force.

2. What is the significance of SO(10) GUT?

The significance of SO(10) GUT lies in its potential to provide a more comprehensive understanding of the fundamental laws of nature. By unifying the three forces, it can explain the relationships between particles and their interactions, and potentially lead to new discoveries in physics. It also has implications for cosmology and the study of the early universe.

3. What are the key features of SO(10) GUT?

Some key features of SO(10) GUT include the prediction of a new type of particle called the "gauge boson", the unification of the three fundamental forces, and the ability to explain the relationships between particles and their interactions. It also incorporates the concept of symmetry breaking, which is essential for understanding the different forces at work in the universe.

4. What is the current status of research on SO(10) GUT?

Research on SO(10) GUT is ongoing and has been a topic of interest for many years. While there is currently no experimental evidence to support the theory, it is still an active area of study and has implications for other areas of physics. Some researchers are also exploring modifications to the original theory to address certain discrepancies and open questions.

5. How does SO(10) GUT compare to other GUTs?

SO(10) GUT is one of many Grand Unified Theories (GUTs) proposed in the field of particle physics. It is considered to be one of the most promising and well-studied GUTs, as it has the ability to unify the three fundamental forces and has been successful in making predictions that have been observed in experiments. However, like other GUTs, it has not yet been proven experimentally and is still a subject of ongoing research and debate.

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