Talks

I will argue that there are quantum states of the field theories of general relativity and electromagnetism that we typically ignore, but have interesting phenomenological effects. These states amount to relaxing the constraint equations known as the Hamiltonian and momentum constraints in GR and Gauss’ law in EM. Turning off the Hamiltonian constraint sources non-dynamical parts of the metric which mimic a pressure-less dust, and thus these effects may be the explanation as to why we have inferred the existence of dark matter, both locally and cosmologically. Turning off the momentum constraints add additional velocity-dependent source terms to this effective dust, but these effects are not conserved and redshift quickly outside the horizon. Turning off the Gauss’ law constraint mimics a charge density that does not respond to electric forces, but follows geodesics, thus adding a charged component to the dust. The effects in electromagnetism may have interesting impacts on BBN, the baryon-photon fluid during and after recombination, galactic dynamics, and cosmic rays. If this new structure in the gravitational and electric fields explain dark matter, it forbids an early period of inflation and therefore requires a different explanation for density perturbations.

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on X^n with logarithmic singularities along the diagonals. Furthermore, we show the pullback of these differential forms to the Fulton-Macpherson compactification space is an isomorphism, thus illustrating a connection between infinitesimal jet spaces of Bun_G(X) and the Lie operad.

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