Aspects of selfdual YangMills and selfdual gravityTools Chattopadhyay, Pratik (2022) Aspects of selfdual YangMills and selfdual gravity. PhD thesis, University of Nottingham.
AbstractIn this thesis, we study the all same helicity loop amplitudes in selfdual YangMills and selfdual gravity. These amplitudes have long been conjectured to be interpreted as an anomaly and are recently linked to the UV divergence of twoloop quantum gravity. In the first part of the thesis, we study the loop amplitudes in selfdual YangMills. We show that the four point oneloop amplitude can be reduced to a computation of shifts, which strongly suggests a case for an anomaly interpretation. We next propose a new formula for the oneloop amplitudes at all multiplicity, in terms of the BerendsGiele currents connected by an effective propagator. We prove the formula by observing that it readily implies the correct collinear properties. To demonstrate the validity of our formula, we do an explicit computation at 3, 4 and 5 points and reproduce the known results. The region momenta variables play an important role in our formula and thus it points to both the worldsheet and the momentum twistor interpretations.
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