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This little write-up is an excellent and beautifully compact description. That said, I would comment that a beginner might be confused by the slightly differing definitions of 'chiral symmetry' that appear:
(1) "This symmetry of the Lagrangian is called flavor symmetry or chiral symmetry, and is denoted as [I'm being sloppy in my use of symbols in this comment]:
U(2)L x U(2)R ..."
(2) [Later...] "The remaining chiral symmetry,
SU(2)L x SU(2)
turns out to be spontaneously broken by quark condensate..."
Isn't it the case that the former (1) is typically called 'flavor symmetry', while the latter (2) is typically called 'chiral symmetry'?
- TLT
