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Friday 16th October 2015 from 10:00 (Europe/Zurich)

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News from the Experiments at CERN (119th Meeting of the SPSC)

OPEN Session 9h00 to 13h15 in the Main Auditorium, followed by CLOSED Session at 14h00 in Georges Charpak Room F, 6th floor, 60-6-015
CERN-SPSC-2015-033; SPSC-A-119

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OPEN Session 9h00 to 13h15 in the Main Auditorium, followed by CLOSED Session at 14h00 in Georges Charpak Room F, 6th floor, 60-6-015 CERN-SPSC-2015-033; SPSC-A-119

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105th meeting of the CMS Collaboration Board (CB105)

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On the CFT Operator Spectrum at Large Global Charge

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 J2 ΔJ - ( J2/2+ J/4 + 3/16) ΔJ-1 - ( J2/2 - J/4 + 3/16) ΔJ+1 = 0.04067 up to corrections that vanish at large J. The spectrum of low-lying excited states is also calculable explicitly: 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 J1/2. The propagation speeds of the Goldstone waves and heavy fermions are (1/√2) and ± 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.

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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 J2 ΔJ - ( J2/2+ J/4 + 3/16) ΔJ-1 - ( J2/2 - J/4 + 3/16) ΔJ+1 = 0.04067 up to corrections that vanish at large J. The spectrum of low-lying excited states is also calculable explicitly: 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 J1/2. The propagation speeds of the Goldstone waves and heavy fermions are (1/√2) and ± 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.