On the CFT operator spectrum at large global charge

DOI10.1007/JHEP12(2015)071zbMATH Open1388.81672arXiv1505.01537OpenAlexW3100516808MaRDI QIDQ2636273

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Publication date: 31 May 2018

Published in: (Search for Journal in Brave)

Abstract: 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 = P h i^{3}

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

D e l t a_{J}

satisfies the sum rule

J^{2} D e l t a_{J} - l e f t (f r a c J^{2} 2 + f r a c J 4 + f r a c 316 i g h t) D e l t a_{J - 1} - l e f t (f r a c J^{2} 2 - f r a c J 4 + f r a c 316 i g h t) D e l t a_{J + 1} = 0.035147

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

D e l t a l l J + s q r t 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^{1 / 2}

. The propagation speeds of the Goldstone waves and heavy fermions are

f r a c 1 s q r t 2

and

p m f r a c 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

.

Full work available at URL: https://arxiv.org/abs/1505.01537

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