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E. Witten, Quantum field theory and the jones polynomial
1989
Earlier work this paper cites.
E. Witten, Gauge Theories and Integrable Lattice Models
1989
Earlier work this paper cites.
N. Y. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups
1990
Earlier work this paper cites.
V. G. Turaev, Skein quantization of poisson algebras of loops on surfaces
1991
Earlier work this paper cites.
L. Chekhov and V. V. Fock, Quantum Teichmuller space
1999
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm
2003
Earlier work this paper cites.
V. Fock and A. Goncharov, Moduli spaces of local systems and higher Teichmuller theory
2006
Earlier work this paper cites.
N. Drukker, D. R. Morrison, and T. Okuda, Loop operators and S-duality from curves on Riemann surfaces
Original
2009
Earlier work this paper cites.
L. F. Alday, D. Gaiotto, and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories
Original
2010
Earlier work this paper cites.

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2016

Gabella, Maxime

We propose a method for determining the spins of BPS states supported on line defects in 4d $\mathcal{N}=2$ theories of class S.

Via the 2d-4d correspondence, this translates to the construction of quantum holonomies on a punctured Riemann surface $\mathcal{C}$.
Our approach combines the technology of spectral networks, which decomposes flat $GL(K,\mathbb{C})$-connections on $\mathcal{C}$ in terms of flat abelian connections on a $K$-fold cover of $\mathcal{C}$, and the skein algebra in the 3-manifold $\mathcal{C}\times [0,1]$, which expresses the representation theory of the quantum group $U_q(gl_K)$.
With any path on $\mathcal{C}$, the quantum holonomy associates a positive Laurent polynomial in the quantized Fock-Goncharov coordinates of higher Teichm\"uller space.

E. Witten, Quantum field theory and the jones polynomial
1989
Earlier work this paper cites.
E. Witten, Gauge Theories and Integrable Lattice Models
1989
Earlier work this paper cites.
N. Y. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups
1990
Earlier work this paper cites.
V. G. Turaev, Skein quantization of poisson algebras of loops on surfaces
1991
Earlier work this paper cites.
L. Chekhov and V. V. Fock, Quantum Teichmuller space
1999
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm
2003
Earlier work this paper cites.
V. Fock and A. Goncharov, Moduli spaces of local systems and higher Teichmuller theory
2006
Earlier work this paper cites.
N. Drukker, D. R. Morrison, and T. Okuda, Loop operators and S-duality from curves on Riemann surfaces
Original
2009
Earlier work this paper cites.
L. F. Alday, D. Gaiotto, and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories
Original
2010
Earlier work this paper cites.