Mathematics Colloquia and Seminars

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The origin of the huge hierarchy between the electroweak and the Planck scales remains the major problem driving the development of particle physics and quantum field theory over the last four decades. I will review the conventional views on its resolution, which is either emergence of new physics at the TeV scale or anthropic fine-tuning. Then I will explore an alternative: the "third way", involving a refined notion of naturalness. I will describe a family of toy UV complete quantum theories providing a proof of concept for this possibility. In these models low energy physics is described by a tuned effective field theory, which exhibits relevant interactions not protected by any symmetries that are separated by an arbitrarily large mass gap from the new gravitational physics, represented by a set of irrelevant operators. Despite this scale separation, the only available language to describe dynamics at all energy scales does not require any fine-tuning. An interesting novel feature of this construction is that UV physics is not described by a fixed point and is governed by a novel type of asymptotic behavior.