Understanding the Higgs mass in string theory
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 attempts within field theory to understand the Higgs mass futile. Even calculations done within string theory fail to 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 perturturbative closed-string vacua. And yet if the UV is tamed by this symmetry then it should be exact even today. In this talk I discuss what can be learned from a fully consistent treatment within a modular invariant theory. Using our framework, I describe how a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, thereby yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. I also discuss a number of critical issues involving the use and interpretation of regulators in UV/IR-mixed theories such as string theory. Finally, I show how the Higgs mass in closed string theories can be recast as a supertrace over only those string states which are physical (i.e., level-matched), thereby al- lowing us to identify a generic “stringy” Coleman-Weinberg potential for the Higgs fields in such theories.
Friday, 12 March 2021, ore 14:30 — Zoom seminar