## Topological effects in particle physics phenomenology

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## Abstract

This thesis is devoted to the study of topological effects in quantum field theories, with a particular focus on phenomenological applications. We begin by deriving a general classification of topological terms appearing in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space `Aharonov-Bohm' (AB) and `

Wess-Zumino' (WZ) terms. We derive a new condition for their

Armed with this classification of topological terms, we then apply it to Composite Higgs models based on a variety of coset spaces

As a further application of our results, we analyse quantum mechanics models featuring such topological terms. In this context, a topological term couples the particle to a background magnetic field. The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. We show how both locality and symmetry can be made manifest, by passing to an otherwise redundant description on a principal bundle over the original configuration space, and by promoting the original symmetry group to a central extension thereof. We then demonstrate how harmonic analysis on the extended symmetry group can be used to solve the Schr{"o}dinger equation.

To conclude our study of topological terms in sigma models, we show that the classification we have proposed may be rigorously justified (and generalised) using differential cohomology theory. In doing so, we introduce the notion of the `

In the remainder of the thesis we depart from the topic of sigma models and turn to gauge theories. We analyse anomalies (which may be understood as arising from topological effects) in both the Standard Model (SM) and theories Beyond the Standard Model (BSM). This analysis consists of two parts, in which we consider `local' and `

global' anomalies in a gauge symmetry

We first chart the space of anomaly-free extensions of the SM by a flavour-dependent

We then turn to global anomalies, which we analyse using the Dai-Freed theorem. Our principal tool here is to compute the bordism groups of the classifying spaces of various Lie groups, preserving particular spin structures, using the Atiyah-Hirzebruch spectral sequence. We show that there are no global anomalies (beyond the Witten anomaly associated with the electroweak factor) in four different `versions' of the SM, in which the gauge group is taken to be