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Four-point correlation modular bootstrap for OPE densities

In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c >> 1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c >> 1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scalar modular bootstrap and zeros of the Riemann zeta function

Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Diagnosis of the Marine Low Cloud Simulation in the NCAR Community Earth System Model (CESM) and the NCEP Global Forecast System (GFS)-Modular Ocean Model v4 (MOM4) coupled model

We present a diagnostic analysis of the marine low cloud climatology simulated by two state-of-the-art coupled atmosphere-ocean models: the NCAR Community Earth System Model (CESM) and the NCEP Global Forecasting System (GFS). In both models, the shallow convection and boundary layer turbulence parameterizations have been recently updated: both models now use a mass-flux scheme for the parameterization of shallow convection, and a turbulence parameterization capable of handling Stratocumulus (Sc)-topped Planetary Boundary Layers (PBLs). For shallow convection, both models employ a convective trigger function based on the concept of convective inhibition and both include explicit convective overshooting/penetrative entrainment formulation. For Sc-topped PBL, both models treat explicitly turbulence mixing and cloud-top entrainment driven by cloud-top radiative cooling. Our focus is on the climatological transition from Sc to shallow Cumulus (Cu)-topped PBL in the subtropical eastern oceans. We show that in the CESM the coastal Sc-topped PBLs in the subtropical Eastern Pacific are well-simulated but the climatological transition from Sc to shallow Cu is too abrupt and happens too close to the coast. By contrast, in the GFS coupled simulation the coastal Sc amount and PBL depth are severely underestimated while the transition from Sc to shallow Cu is ³delayed² and offshore Sc cover is too extensive in the subtropical Eastern Pacific. We discuss the possible connections between such differences in the simulations and differences in the parameterizations of shallow convection and boundary layer turbulence in the two models.

Xiao, Heng↗