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  1. A bstract We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term — which resembles the linear Einstein action — dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete — the relevant symmetries can be viewed as emergent — nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries. 
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  2. A bstract We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an SO(4 , 2) group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of Love numbers. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations. 
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  3. The precision cosmological model describing the origin and expansion history of the universe, with observed structure seeded at the inflationary cosmic horizon, demands completion in the ultraviolet and in the infrared. The dynamics of the cosmic horizon also suggests an associated entropy, again requiring a microphysical theory. Recent years have seen enormous progress in understanding the structure of de Sitter space and inflation in string theory, and of cosmological observables captured by quantum field theory and solvable deformations thereof. The resulting models admit ongoing observational tests through measurements of the cosmic microwave background and large-scale structure, as well as through analyses of theoretical consistency by means of thought experiments. This paper, prepared for the TF01 and TF09 conveners of the Snowmass 2021 process, provides a synopsis of this important area, focusing on ongoing developments and opportunities. Note: Contribution to Snowmass 2021 
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  4. Abstract It is well known that asymptotically flat black holes in generalrelativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governingstatic (spin 0,1,2)perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions,and derive their general properties: (1) solutions that decay withradius spontaneously break the symmetries, and mustdiverge at the horizon;(2) solutions regular at the horizon respect the symmetries, andtake the form of a finite polynomial that grows with radius.Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probesthe worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved. 
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