Abstract:We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, AharonovBohm effects record the "tracks" of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.

Cosmic Inflation provides an attractive framework for understanding the early universe and the cosmic microwave background. It can readily involve energies close to the scale at which Quantum Gravity effects become important. General considerations of black hole quantum mechanics suggest nontrivial constraints on any effective field theory model of inflation that emerges as a low-energy limit of quantum gravity, in particular the constraint of the Weak Gravity Conjecture. We show that higher-dimensional gauge and gravitational dynamics can elegantly satisfy these constraints and lead to a viable, theoretically-controlled and predictive class of Natural Inflation models.The success of modern cosmology is founded on the simplifying features of homogeneity, isotropy and spatial flatness of the Universe on the largest distances. In this limit, spacetime evolution is given in terms of a single scale-factor, a(t), and its Hubble expansion rate, H ≡ȧ/a. Homogeneity and flatness are themselves puzzling, constituting very special "initial" conditions from the viewpoint of the Hot Big Bang (HBB). But they become more robust if the HBB is preceded by an even earlier era of Cosmic Inflation, exponential expansion of the Universe driven by the dynamics of a scalar field φ (the "inflaton") coupled to General Relativity (see [1] for a review):(We work in fundamental units in which = c = 1. G N is Newton's constant.) If "slow roll" is achieved for a period of time,φ subdominant and V (φ) ≈ constant, we get a ∝ e Ht , H ≈ constant, after which the potential energy is released, "reheating" the Universe to the HBB. Phenomenologically, N e-folds > 40−60 are required to understand the degree of homogeneity/flatness we see today.Remarkably, quantum fluctuations during inflation can seed the inhomogeneities in the distribution of galaxies and in the Cosmic Microwave Background (CMB). In particular, the CMB temperature-fluctuation powerspectrum,is generically predicted by inflation to be approximately scale-invariant, n s ≈ 1, and is measured to be n s ≈ 0.96 [2,3].Slow roll itself requires an unusually flat potential, suggesting that the inflaton φ is a pseudo-Nambu-Goldstone boson of a spontaneously broken global U (1) symmetry, an "axion". If there is a weak coupling that explicitly violates U (1) symmetry by a definite amount of charge, one can generate a potential,where f is a constant determined by the spontaneous breaking dynamics, while V 0 is a constant proportional to the weak coupling. This is the model of "Natural Inflation" [4]. 1 It can be successfully fit to data, and in particular for N e-folds > 50, n s ≈ 0.96, one findsThe Planck scale M pl ≡ 1/ √ 8πG N = 2 × 10 18 GeV is the energy scale above which Quantum Gravity (QG) effects become strong, and effective field theory (EFT) must break down in favor of a more fundamental description such as superstring theory [6].The very high energy scale V 1/4 0 ≈ 0.01M pl is without precedent in observational physics and implies sensitivity to new exotic phenomena. For such large ...

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L₀) in quasi-two-dimensional systems, while in three dimensions it scales as L₀⁻¹ - L⁻¹, where L₀ is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is enhanced because of long-range correlations between concentration fluctuations and fluctuations of the velocity parallel to the concentration gradient. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L 0 ) in quasi-two dimensional systems, while in three dimensions it grows as L −1 0 − L −1 , where L 0 is a reference length. The predictions of a simple fluctuating hydrodynamics theory, closely related to second-order mode-mode coupling analysis, are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. We elucidate the direct connection to the long-time tail of the velocity autocorrelation function in finite systems, as well as finite-size corrections employed in molecular dynamics calculations. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.