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We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number n of fundamental representations of SU(N), and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of SU(N) to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-n limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.
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Phase transitions in the decomposition of SU(N) representations
We study the multiplicity of irreducible representations in the decomposition of π fundamentals of ππ(π) weighted by a power of their dimension in the large π and large π double scaling limit. A nontrivial scaling is obtained by keeping πβπ2 fixed, which plays the role of an order parameter. We find that the system generically undergoes a fourth order phase transition in this parameter, from a dense phase to a dilute phase. The transition is enhanced to third order for the unweighted multiplicity, and disappears altogether when weighting with the first power of the dimension. This corresponds to the infinite temperature partition function of non-Abelian ferromagnets, and the results should be relevant to the thermodynamic limit of such ferromagnets at high temperatures.
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- Award ID(s):
- 2112729
- PAR ID:
- 10532711
- Publisher / Repository:
- Nuclear Physics B
- Date Published:
- Journal Name:
- Nuclear Physics B
- Volume:
- 999
- Issue:
- C
- ISSN:
- 0550-3213
- Page Range / eLocation ID:
- 116434
- Subject(s) / Keyword(s):
- Nonabelian, large-N, phase transitions, SU(N), representations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.nuclphysb.2023.116434
