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Walking Beyond the Standard Model

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There are good reasons to think that our understanding of particle physics is incomplete. The effective field theory describing the particles that we know about breaks down at the TeV scale, and new effective degrees of freedom must enter. In this talk I will discuss the role that strong dynamics might play in this new physics, focusing on the ways in which approximately scale-invariant dynamics could explain puzzling features of our low-energy Lagrangian. I will also describe recent theoretical and numerical results aimed at constraining the range of behavior that can occur in 4D conformal field theories.