Higher Form Gauge Theories

My MSc thesis, under the guidance of Dr Karapet Mkrtchyan at Imperial College London.

I studied his work on the democratic formulation of higher-form electromagnetism with non-linear deformations, the encoding of this formulation in a one-higher-dimensional topological theory, and the use of both of these techniques for chiral forms.

Anomaly Inflow: Multiple global symmetries can have ‘t Hooft anomalies which prevent gauging them simultaneously. This also occurs in higher-form electromagnetism. One way to treat this is to include a ‘Symmetric Topological Phase’ in the theory, which does not affect the dynamics but cancels the ‘t Hooft anomaly. This phase is the integral over a one-higher-dimensional manifold, which has the spacetime as its boundary. Dr Mkrtchyan’s work occurs in a similar context and so may allow a better understanding of anomaly inflow.

Generalised Symmetries and SymmTFTs: Higher-form electromagnetism is built upon a differential-form-like gauge symmetry, which is one of the kinds of non-group symmetries which are explored in the field of generalised symmetries. There has been considerable progress in recent years in understanding these broader ideas of what symmetries can be, connecting them to topological operators (‘Symmetry Defect Operators’) and also using one-higher-dimensional topological theories to encode, define and exploit the symmetries of a theory (‘SymmTFT’, i.e. Symmetry Topological Field Theory). I am reading about these ideas and looking for problems connected to my advisor’s work. I have previously studied Topological Quantum Field Theories; see TQFTs.

I am also looking into generalising the Stueckelberg formulation to \(p\)-form fields and exploring the consistent quantisation of such a theory.