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I am looking for examples where only one Goldstone boson appears after spontaneous breaking of 2 different symmetries.

In this post there is an answer why there are no Goldstone bosons for rotational symmetry on a lattice. I am interested in examples for continuous systems.

Question is inspired by this talk by Sieberg, more precisely by statement around 1:19:00.

Nikita
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  • Thank you! Could you post concrete links to references? – Nikita Apr 09 '20 at 02:54
  • Manohar & Low. Track citations thereto. – Cosmas Zachos Apr 09 '20 at 13:07
  • Might read up on Brauner, T., 2010, Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems, Symmetry, 2 (2), pp.609-657. – Cosmas Zachos Apr 09 '20 at 13:15
  • @CosmasZachos Thank you! I don't get idea and exploration yet, maybe you can help me with it, I think that essence very intuitive. But, your examples about space-time symmetry, as I understand. Does it mean, that such phenomena can't occur in internal of gauge symmetry? – Nikita Apr 09 '20 at 20:06
  • For fully Lorentz invariant theories and SSBroken internal symmetries, one broken generator per goldston, as you may read up in QFT books. Your question is spectacularly orthogonal to that. – Cosmas Zachos Apr 09 '20 at 20:41
  • @CosmasZachos What about example in Maxwell theory, when electric and magnetic two form symmetries are both broken in Coulomb phase, but Goldstone boson only one -- photon? – Nikita Apr 09 '20 at 20:51
  • @CosmasZachos , I edited question – Nikita Apr 09 '20 at 22:03
  • Ugh! your are really talking about NS's 1-form symmetries, not ordinary standard textbook QFT internal symmetries! He's reformulated the entire landscape. In plain Lorentz invariant QFT the goldston to broken-internal-symmetry counting still holds. – Cosmas Zachos Apr 09 '20 at 22:12
  • @CosmasZachos , No. Did you watch fragment of video around 1:19:00? Exist 2 1-form symmetries, and they both are broken in Coulomb phase, but particle only one! – Nikita Apr 09 '20 at 22:19
  • I can't help you. I strongly believe you are "misreading" him. Weinberg's QFT book II, p173 & 295 reviews the standard picture for conventional scalar Noether *independent* symmetry charges. You may speculate with Natti on 1-form ones, and fall for his glib evasions, but that is far beyond the context of mainstream relativistic QFT. Condensed matter breaks Lorentz invariance; and Natti calls membrane physics "particle physics", a broad stretch. Weinberg's book, or Coleman's lectures, the "owners" of the field. – – Cosmas Zachos Apr 10 '20 at 00:17

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