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Moduli spaces of vacua are an intriguing property of certain supersymmetric QFTs which have been widely explored. However, a first-principles approach to moduli spaces and how they constrain observables is still lacking. This question is even more pressing due to recent interest in moduli spaces in theories with only two supercharges, where supersymmetry is extremely weak and does not allow for exact computations. In this talk we attempt to bootstrap conformal field theories with moduli spaces. First we assume an additional global symmetry which is spontaneously broken along the moduli space, and use techniques from the large charge expansion to show that the existence of a moduli space directly constrains CFT data of charged operators. We then study the generic case by using a "moduli space bootstrap equation" to write down perturbative sum rules on observables of CFTs order-by-order in a small coupling. We discuss several examples and applications of our results. 

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Theories which spontaneously break spacetime parity can solve the strong CP problem. They usually have few free parameters and are therefore very predictive, but their landscape remains quite unexplored. I will present a construction based on a complete mirror copy of the standard model, linked to our world by colored portal fields. Those induce the partial spontaneous breaking of the color groups, yielding a vanishing theta angle at low energies. The lightest BSM fields could be found at colliders, and are either colored (pseudo-Goldstone or vector) bosons, or some of the vectorlike fermions predicted by parity. The lightest of the latter can actually play the role of thermal dark matter in our model, unlike what was previously found in similar constructions.

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This talk is virtual, but will also be broadcast in the Sky Room. 

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The growth of cosmic structures provides a bridge between observations and theories. In the first part of this talk, I will review the sigma8 tension between early- and late-time measurements of cosmic structure growth, and its physical implications. Are we seeing a chink in the standard cosmological model’s armor? To unveil the origin of this tension (and possibly new physics in the late Universe), galaxy clustering and spectroscopic surveys will play an indispensable role. In the second part of the talk, I will introduce a novel framework to extract cosmological information from millions of galaxies in spectroscopic surveys, directly at the field level—i.e. the three-dimensional map level with millions of grid points. The goal is to achieve a percent-level constraint on sigma8 and growth of structure with stage-IV surveys like DESI. I will further discuss recent progress towards this goal, highlighting latest breakthroughs, results in a community data challenge, and remaining challenges.

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