Week 15.02.2015 – 21.02.2015

It is often said that soliton contributions to perturbative processes in QFT are exponentially suppressed by a form-factor. We will provide a derivation of this form-factor by studying the soliton-antisoliton pair-production amplitude. This reduces to the calculation of a matrix element in the quantum mechanics on the soliton moduli space. We will investigate the conditions under which the latter leads to suppression. Extending this framework to instanton-solitons in five-dimensional Yang-Mills theory leaves open the possibility that such contributions will not be suppressed.

We review the construction of the so-called λ-deformations of WZW and gauged WZW models. We discuss their integrability and algebraic properties, their behavior under RG flows as well as their embeddings to type-II supergravity.

A central outcome of the recent Higgs discovery is that the Standard Model (SM) appears to be a selfconsistent quantum field theory all the way up to the Planck scale. Moreover, the measured values for the Higgs and top masses have an intriguing consequence for the question of stability of the Higgs vacuum: The SM lies close to the border of absolute electroweak vacuum stability and metastability. However, these celebrated results extrapolate the SM into a region where quantum gravity effects become important. We have therefore computed the quantum gravitational contributions to the standard model effective potential and analyzed their effects on the Higgs vacuum stability in the framework of effective field theory. Non-renormalizability of Einstein gravity induces higher dimension φ6 and φ8 operators at the one- loop level with novel couplings η1/2. We find that the true minimum of the standard model effective potential now lies below the Planck scale for almost the entire parameter space (η1/2(mt) > 0.01). In addition quantum gravity is shown to contribute to the minimal value of the standard model NLO effective potential at the percent level. The quantum gravity induced contributions yield a metastable vacuum for a large fraction of the parameter space in the flowing couplings η1/2.