On the CFT operator spectrum at large global charge

By S. Hellerman, D. Orlando, S. Reffert, Masataka Watanabe. 2015

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A bstractWe calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−J22+J4+316ΔJ−1−J22+J4+316ΔJ+1=0.04067$$ {J}^2{\varDelta}_J-\left(\frac{J^2}{2}+\frac{J}{4}+\frac{3}{16}\right){\varDelta}_{J-1}-\left(\frac{J^2}{2}+\frac{J}{4}+\frac{3}{16}\right){\varDelta}_{J+1}=0.04067 $$ up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3$$ {\varDelta}_J+\sqrt{3} $$. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12$$ {J}^{+\frac{1}{2}} $$. The propagation speeds of the Goldstone waves and heavy fermions are 12$$ \frac{1}{\sqrt{2}} $$ and ±12$$ \pm \frac{1}{2} $$ times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8b5ae237c9f9a7f099e3a1add48dbb0be3bd734a