In Polchinski String Vol 1:

Chiral gauge couplings. The gauge interactions in nature are parity asymmetric (chiral). This has been a stumbling block for a number of previous unifying ideas: they required parity symmetric gauge couplings. String theory allows chiral gauge couplings.

What are the approaches from String theory allowing chiral gauge couplings?

Can experts sketch and enumerate all of the different ideas?

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    $\begingroup$ The gauge interactions in nature are parity asymmetric (chiral). Is there parity asymmetry in QCD? $\endgroup$ – G. Smith Oct 17 '20 at 21:14
  • $\begingroup$ >> parity asymmetry in QCD. Ans: No $\endgroup$ – ann marie cœur Oct 17 '20 at 21:41
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    $\begingroup$ So I don’t understand this sweeping statement about “the gauge interactions in nature”, which seems plainly wrong. Why didn’t Polchinski write “some gauge interactions in nature”? Is there some context that you omitted? $\endgroup$ – G. Smith Oct 17 '20 at 21:47
  • $\begingroup$ He meant the whole gauge interaction violates P. I just copy paste $\endgroup$ – ann marie cœur Oct 18 '20 at 0:27

Is there a classification of all theories belonging to the string landscape with chiral gauge couplings? No, we are far from such a precise knowledge of the string theory landscape.

Nevertheless, a sample of representative approaches can be mentioned:

1) Heterotic string compactifications on Calabi-Yau: See Chiral four-dimensional heterotic strings from self-dual lattices.

2) Four-dimensional $N=1$ superconformal quiver gauge theories: See brane tillings and their applications. The simplest cases of this class of theories are dicussed in the case of local Calabi-Yau, however, they model the local behaviour of a wide class of semi-realistic theories.

3) Intersecting branes setups: See the excellent review https://arxiv.org/abs/hep-th/0502005.

4) F-theory compactifications: See the outstanding A Quadrillion Standard Models from F-theory.

5) Strings on orbifold geometries: See strings on orbifolds.

Just to mention a few.


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