More Like this

1. A Puzzle About General Covariance and Gauge

   https://doi.org/10.1086/736478  

   March, Eleanor; Weatherall, James (May 2025, The British Journal for the Philosophy of Science)

   We consider two simple criteria for when a physical theory should be said to be ``generally covariant'', and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural. We then show how these observations relate to previous arguments about the significance of solder forms in assessing disanalogies between general relativity and Yang-Mills theory. We conclude by suggesting that general covariance is really about functoriality. 

   more » « less
2. The Parameter Dependence of Eddy Heat Flux in a Homogeneous Quasigeostrophic Two-Layer Model on a β Plane with Quadratic Friction

   https://doi.org/10.1175/JAS-D-20-0145.1  

   Chang, Chiung-Yin; Held, Isaac M. (January 2021, Journal of the Atmospheric Sciences)

   null (Ed.)

   Abstract This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a β plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer f -plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, −5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, −7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both and the strength of the frictional drag, , are much smaller than unity (here, c D is the nondimensional drag coefficient divided by the depth of the layer, k d is the wavenumber of deformation radius, and U is the imposed background vertical wind shear). For values of and that are closer to one, the theory works only if the full spectrum shape of the eddy kinetic energy is given. Despite the qualitative, fitting nature of this approach and its failure to explain the full parameter range, we believe its documentation here remains useful as a reference for the future attempt in pursuing a better theory. 

   more » « less
3. Yang-Mills as a Liouville theory

   https://doi.org/10.1016/j.physletb.2023.138229  

   Stieberger, Stephan; Taylor, Tomasz R; Zhu, Bin (November 2023, Physics Letters B)

   We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the one-loop coefficient of the Yang-Mills beta function. 

   more » « less
4. Towards a quantum field theory description of nonlocal spacetime defects

   https://doi.org/10.1088/1361-6382/ad36a6  

   Carone, Christopher D; Donald, Noah L (April 2024, Classical and Quantum Gravity)

   We propose an ansatz for encoding the physics of nonlocal spacetime defects in the Green’s functions for a scalar field theory defined on a causal set. This allows us to numerically study the effects of nonlocal spacetime defects on the discrete Feynman propagator of the theory defined on the causal set in 1+1 dimensions, and to compare to the defect-free limit. The latter approaches the expected continuum result, on average, when the number of points becomes large. When defects are present, two points with the same invariant spacetime interval can have different propagation amplitudes, depending on whether the propagation is between two ordinary spacetime points, two defects, or a defect and an ordinary point. We show that a coarse-grained description that is only sensitive to the average effect of the defects can be interpreted as a defect-induced mass and wave-function renormalization of the scalar theory. 

   more » « less
5. The Control of Surface Friction on the Scales of Baroclinic Eddies in a Homogeneous Quasigeostrophic Two-Layer Model

   https://doi.org/10.1175/JAS-D-18-0333.1  

   Chang, Chiung-Yin; Held, Isaac M. (June 2019, Journal of the Atmospheric Sciences)

   In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales was proposed by Held in 1999 in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations. 

   more » « less