Astronomers use interferometry to observe and study objects in the sky. The early evidence for compact objects like black holes and neutron stars came from radioastronomy. More recently the Event Horizon Telescope has imaged a black hole in the centre of M87 using VLBI (very long baseline interferometry).These observations are important to fundamental physics as they push the limits of our understanding. However these interferometric observations are dogged by noise, which can alter the amplitude and phase of the signal received at each telescope. This noise introduces spurious effects which come in the way of getting an accurate image of the object in the sky. There is a need for extracting information from the measurements which is immune to such distortions. Astronomers call these quantities closure phases and closure amplitudes. The current state of understanding of such quantities is incomplete, especially in the case of polarised observations, which would be needed to understand the magnetic field structure of a source. This is where fundamental physics can help astronomers. I will describe recent progress in understanding closure invariants in terms of gauge theory. The theory of Wilson loops (aka gauge theory, Geometric Phase, anholonomy,loop variables) permits us the identify a complete and independent set of closure quantities. Our treatment gives a unified view of closure phases and closure amplitudes and sets the theory on a firm mathematical basis.
The ICTS Math-Phys series are virtual seminars at the intersection of mathematics (geometry, algebra, representation theory, higher categories, TQFT, ...) and theoretical physics (QFT, string theory, condensed matter, ...). The purpose of this series is to bring together mathematicians and physicists around topics of common interest and foster interdisciplinary discussions.
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