On the CFT operator spectrum at large global charge

Hellerman, Simeon; Orlando, Domenico; Reffert, Susanne; Watanabe, Masataka (2015). On the CFT operator spectrum at large global charge. Journal of High Energy Physics, 2015(12), pp. 1-34. Springer 10.1007/JHEP12(2015)071

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We 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+316)ΔJ−1−(J22+J4+316)ΔJ+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√. 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. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Institute of Theoretical Physics
10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)

UniBE Contributor:

Orlando, Domenico and Reffert, Susanne

Subjects:

500 Science > 530 Physics

ISSN:

1029-8479

Publisher:

Springer

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

15 Feb 2016 15:30

Last Modified:

28 May 2017 02:03

Publisher DOI:

10.1007/JHEP12(2015)071

BORIS DOI:

10.7892/boris.75457

URI:

https://boris.unibe.ch/id/eprint/75457

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