A bstract We study operators with large charge j in the d dimensional O ( N ) model with long range interactions that decrease with the distance as 1/ r d + s , where s is a continuous parameter. We consider the double scaling limit of large N , large j with $$ j/N=\hat{j} $$ j / N = j ̂ fixed, and identify the semiclassical saddle point that captures the twopoint function of the large charge operators in this limit. The solution is given in terms of certain ladder conformal integrals that have recently appeared in the literature on fishnet models. We find that the scaling dimensions for general s interpolate between $$ {\Delta }_j\sim \frac{\left(ds\right)}{2}j $$ ∆ j ∼ d − s 2 j at small $$ \hat{j} $$ j ̂ and $$ {\Delta }_j\sim \frac{\left(d+s\right)}{2}j $$ ∆ j ∼ d + s 2 j at large $$ \hat{j} $$ j ̂ , which is a qualitatively different behavior from the one found in the short range version of the O ( N ) model. We also derive results for the structure constants and 4point functions with two large charge and one or two finite charge operators. Using a description of the long range models as defects in a higher dimensional local free field theory, we also obtain the scaling dimensions in a complementary way, by mapping the problem to a cylinder in the presence of a chemical potential for the conserved charge.
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Approaching the Conformal Limit of Quark Matter with Different Chemical Potentials
We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zerotemperature limit reaches the conformal limit. We discuss the influence of nonzero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zeronet strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. We find that the inclusion of all quark masses (even the light ones) can produce different results depending on the chemical potential values or constraints assumed. A positive or negative deviation of 10% from the pressure of free massless quarks with the same chemical potential was found to take place as low as μB=77 to as high as 48,897 MeV. This illustrates the fact that the “free” or conformal limit is not a unique description. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit.
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 Award ID(s):
 1748621
 NSFPAR ID:
 10521523
 Publisher / Repository:
 MDPI
 Date Published:
 Journal Name:
 Symmetry
 Volume:
 16
 Issue:
 7
 ISSN:
 20738994
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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