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A bstract The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ > 0. Recently, we constructed families of operators in the BLS and showed that they transform as conformal primary operators. In this paper we provide an explicit expression for the BLS stress-energy tensor and compute its operator product expansion with other operators. Our results are consistent with the conformal Ward identities and our previous result that the central charge is c = 2 λ . In the case of domains with boundary we identify a boundary operator that has properties consistent with the boundary stress-energy tensor. We show that this operator generates local deformations of the boundary and that it is related to a boundary operator that induces a Brownian excursion starting or ending at its insertion point. 

Abstract We investigate the fine-structure [Cii] line at 158μm as a molecular gas tracer by analyzing the relationship between molecular gas mass (M_mol) and [Cii] line luminosity (L_[CII]) in 11,125z≃ 6 star-forming, main-sequence galaxies from thesimbasimulations, with line emission modeled by the Simulator of Galaxy Millimeter/Submillimeter Emission. Though most (∼50%–100%) of the gas mass in our simulations is ionized, the bulk (>50%) of the [Cii] emission comes from the molecular phase. We find a sublinear (slope 0.78 ± 0.01) $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log M_{\mathrm{mol}}$relation, in contrast with the linear relation derived from observational samples of more massive, metal-rich galaxies atz≲ 6. We derive a median [Cii]-to-M_molconversion factor ofα_[CII]≃ 18M_⊙/L_⊙. This is lower than the average value of ≃30M_⊙/L_⊙derived from observations, which we attribute to lower gas-phase metallicities in our simulations. Thus, a lower, luminosity-dependent conversion factor must be applied when inferring molecular gas masses from [Cii] observations of low-mass galaxies. For our simulations, [Cii] is a better tracer of the molecular gas than COJ= 1–0, especially at the lowest metallicities, where much of the gas isCO-dark. We find thatL_[CII]is more tightly correlated withM_molthan with star formation rate (SFR), and both the $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log M_{\mathrm{mol}}$and $\log L_{\left[\mathrm{C}\mathrm{II}\right]}–\log \mathrm{SFR}$relations arise from the Kennicutt–Schmidt relation. Our findings suggest thatL_[CII]is a promising tracer of the molecular gas at the earliest cosmic epochs.