Twist Fields in Quantum Field Theory: Entanglement Measures and Pentagonal Amplitudes

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Branch point twist fields play an important role in the study of measures of entanglement such as the Rényi entropies and the Negativity. In 1+1 dimensions such measures can be written in terms of multi-point functions of branch point twist fields. For 1+1-dimensional integrable quantum field theories and also in conformal field theory much is known about how to compute correlation functions and, with the help of the twist field, this knowledge can be exploited in order to gain new insights into the properties of various entanglement measures. In this talk I will review some of our main results in this context.

I will then go on to introduce a new (related) class of fields we have recently named conical twist fields. These are fields whose two-point functions have (surprisingly) been found to describe gluon amplitudes in the strong coupling limit of super Yang-Mills theories and therefore have featured in a completely different context from that of entanglement measures. Interestingly, at critical points, branch point and conical twist fields have the same conformal dimension and beyond criticality they also have very similar form factors, however they are different in many other respects.  In my talk I will discuss and justify some of their similarities and differences.