Speaker
Description
Most of the computational evidence for the Bose–Fermi duality of fundamental fields coupled to $U(N)$ Chern–Simons theories originates in the large-N calculations performed in the light-cone gauge. The evaluation of the thermal free energy on a finite-sized sphere is elusive in the light-cone gauge but more natural in another gauge, the ‘temporal’ gauge. We use it to evaluate the finite-temperature partition function of $U(N)$ and $SU(N)$ coupled fermions at large N and finite chemical potential on $S^2$, a novel physical setting for the problem. We set up the finite-temperature gap equations, solve them, and evaluate the partition function, closely following the tricks explored in [arXiv:2307.11020], where we work out the results on $\mathbb{R}^2$ at large N, which demonstrate perfect agreement with the earlier lightcone gauge results. We find new formulae for the dynamically generated and flux-dependent masses (a completely novel feature with no flat-space counterpart). We look forward to announcing the second installment of our work soon.
