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Compensating strong coupling with large charge. (English) Zbl 1378.81099

Summary: We study some (conformal) field theories with global symmetries in the sector where the value of the global charge \(Q\) is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone’s theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [S. Hellerman et al., J. High Energy Phys. 2015, No. 12, Paper No. 71, 34 p. (2015; Zbl 1388.81672)], that the effective field theory describing such sector of fixed \(Q\) contains effective couplings \(\lambda_{\mathrm{eff}} \sim \lambda^{b}/Q^{a}\), where \(\lambda\) is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the \(O(n)\) model in this limit.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R40 Symmetry breaking in quantum theory

Citations:

Zbl 1388.81672
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References:

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