Lectures

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2017/09/11

15:30-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jean Zinn-Justin (CEA Saclay)
3D field theories with Chern-Simons term for large N in the Weyl gauge (ENGLISH)
[ Abstract ]
ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.
We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.
We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.
Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.