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Time: Wed 4 pm - 5:30 pm ET, Feb 14
Location: Harvard CMSA G10
Zoom:
https://harvard.zoom.us/j/977347126Password: cmsa
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Sen Hu (Shanghai Institute for Mathematics and Interdisciplinary Study)
Title: Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
Abstract: In this talk we discuss the algebra of quantum observables
of the Chern-Simons matrix model which was originally proposed by
Susskind and Polychronakos to describe electrons in fractional quantum
Hall effects. We establish the commutation relations for its
generators and study the large N limit of its representation. We show
that the large N limit algebra is isomorphic to the uniform in N
algebra studied by Costello, which is conjecturally isomorphic to the
deformed double current algebra studied by Guay. Under appropriate
scaling limit, we show that the large N limit algebra degenerates to a
Lie algebra which admits a surjective map to the affine Lie algebra of
u(p). This leads to a complete proof of the large N emergence of the
u(p) current algebra as proposed by Dorey, Tong and Turner. This also
suggests a rigorous derivation of edge excitation of a fractional
quantum Hall droplet. This is a joint work with Si Li, Dongheng Ye and
Yehao Zhou (arXiv: 2308.14046).