Regular Seminar Steve Abel (Durham)
Almost all existing calculations that concern the Higgs mass are performed within the framework of an effective field theory. While sufficient for certain purposes, such calculations throw up problems to do with fine-tuning and naturalness in particular the famous hierarchy problem. This makes most attempts within field theory to understand the Higgs mass pretty much futile. Even most phenomenology done within string theory does not respect the full string symmetries that are responsible for many of the remarkable finiteness properties for which string theory is famous. Chief among these symmetries is worldsheet modular invariance, which is an exact symmetry of all perturtubative closed-string vacua. And yet if the UV is tamed by this symmetry then it should be exact even today! In this talk I will discuss the many things one can learn from this fact. For example that a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. In addition one learns about the use and interpretation of modular invariant regulators in string theory, which in turn dictates how string theory arranges its UV/IR-mixing to make itself finite. Finally, I discuss how the effective field theory emerges showing that ultimately the Higgs mass can be understood as arising from an infinite â€œstringyâ€ sum of Coleman-Weinberg effective potentials in such theories. The results can therefore serve as the launching point for a rigorous investigation of hierarchy problems in a UV complete theory.