Fetching the paper…
Reading the bibliography…
We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3.
K. G. Wilson, “Confinement of quarks,” Phys. Rev. D 10
1974
Earlier work this paper cites.
J. Villain, “Theory of one-dimensional and two-dimensional magnets with an easy magnetization plane. 2. The Planar, classical, two-dimensional magnet,” J. Phys. (France) 36
1975
Earlier work this paper cites.
J. B. Kogut and L. Susskind, “Hamiltonian Formulation Of Wilson’s Lattice Gauge Theories,” Phys. Rev. D 11
1975
Earlier work this paper cites.
A. A. Migdal, “Gauge transitions in gauge and spin lattice systems,” Sov. Phys. JETP 42
1975
Earlier work this paper cites.
L. P. Kadanoff, “Notes On Migdal’s Recursion Formulas,” Annals Phys. 100
1976
Earlier work this paper cites.
B. Kostant, ”On MacDonald’s η \eta - Function Formula, the Laplacian and Generalized Exponents,” Adv. in Math., 20, 179-212 (1976)
1976
Earlier work this paper cites.
T. Banks, R. Myerson and J. B. Kogut, “Phase Transitions In Abelian Lattice Gauge Theories,” Nucl. Phys. B 129
1977
Earlier work this paper cites.
J. V. Jose, L. P. Kadanoff, S. Kirkpatrick and D. R. Nelson, “Renormalization, vortices, and symmetry breaking perturbations on the two-dimensional planar model,” Phys. Rev. B 16
1977
Earlier work this paper cites.
A. M. Polyakov, “Thermal Properties Of Gauge Fields And Quark Liberation,” Phys. Lett. B 72
1978
Earlier work this paper cites.
M. E. Peskin, “Mandelstam ’T Hooft Duality In Abelian Lattice Models,” Annals Phys. 113
1978
Earlier work this paper cites.
L. Susskind, “Lattice Models Of Quark Confinement At High Temperature,” Phys. Rev. D 20
1979
Earlier work this paper cites.
M. Stone, “Lattice Formulation Of The Cp**(N-1) Nonlinear Sigma Models,” Nucl. Phys. B 152
1979
Earlier work this paper cites.
I. Bars and F. Green, “Complete Integration Of U(N) Lattice Gauge Theory In A Large N Limit,” Phys. Rev. D 20
1979
Earlier work this paper cites.
N. S. Manton, “An Alternative Action For Lattice Gauge Theories,” Phys. Lett. B 96
1980
Earlier work this paper cites.
D. J. Gross and E. Witten, “Possible third order phase transition in the large N N lattice gauge theory,” Phys. Rev. D 21
1980
Earlier work this paper cites.
S. R. Wadia, “N = Infinity Phase Transition In A Class Of Exactly Soluble Model Lattice Gauge Theories,” Phys. Lett. B 93
1980
Earlier work this paper cites.
P. Menotti and E. Onofri, “The Action Of SU(N) Lattice Gauge Theory In Terms Of The Heat Kernel On The Group Manifold,” Nucl. Phys. B 190
1981
Earlier work this paper cites.
E. Onofri, “SU(N) Lattice Gauge Theory With Villain’s Action,” Nuovo Cim. A 66
1981
Earlier work this paper cites.
C. B. Lang, P. Salomonson and B. S. Skagerstam, “A Study Of Exactly Solvable Lattice Gauge Theories In Two Space-Time Dimensions,” Phys. Lett. B 100
1981
Cited alongside, same era.
C. B. Lang, P. Salomonson and B. S. Skagerstam, “Large N Lattice Gauge Theory Without Third Order Phase Transition,” Nucl. Phys. B 190
1981
Cited alongside, same era.
H. Neuberger, “Nonperturbative Contributions In Models With A Nonanalytic Behavior At Infinite N,” Nucl. Phys. B 179
1981
Cited alongside, same era.
W. Janke and H. Kleinert, “How Good Is The Villain Approximation?,” Nucl. Phys. B 270
1986
Cited alongside, same era.
E. Witten, “Quantum field theory and the Jones polynomial,” Commun. Math. Phys. 121
1989
Cited alongside, same era.
S. de Haro and M. Tierz, “Brownian motion, Chern-Simons theory, and 2 D 2D Yang-Mills,” Phys.Lett. B 601
2004
Later among the works it cites.
M. Mariño, “Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants,” Commun. Math. Phys. 253
2004
Later among the works it cites.
T. Okuda, “Derivation of Calabi-Yau crystals from Chern-Simons gauge theory,” J. High Energy Phys. 0503
2005
Later among the works it cites.
M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, “Black holes, q q -deformed 2 D 2D Yang-Mills, and non-perturbative topological strings,” Nucl. Phys. B 715
2005
Later among the works it cites.
C. Beasley and E. Witten, “Non-abelian localization for Chern-Simons theory,” J. Diff. Geom. 70
2005
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
V. Periwal and D. Shevitz, “Unitary matrix models as exactly solvable string theories,” Phys. Rev. Lett. 64
1990
Cited alongside, same era.
B. E. Rusakov, “Loop averages and partition functions in U ( N ) U(N) gauge theory on two-dimensional manifolds,” Mod. Phys. Lett. A 5
1990
Cited alongside, same era.
E. Witten, “Gauge Theories, Vertex Models and Quantum Groups,” Nucl. Phys. B 330
1990
Cited alongside, same era.
M. L. Mehta, Random Matrices
1991
Cited alongside, same era.
M. Blau and G. Thompson, “Derivation of the Verlinde formula from Chern-Simons theory and the G/G model,” Nucl. Phys. B 408
1993
Cited alongside, same era.
S. Cordes, G. W. Moore and S. Ramgoolam, “Lectures on 2 D 2D Yang-Mills theory, equivariant cohomology and topological field theories,” Nucl. Phys. Proc. Suppl. 41
1995
Cited alongside, same era.
J. Fuchs, Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory (Cambridge University Press, 1995)
1995
Cited alongside, same era.
M. Marino, “Chern-Simons theory and topological strings,” Rev. Mod. Phys. 77
2005
Later among the works it cites.
M. Blau and G. Thompson, “Chern-Simons theory on S 1 S^{1} -bundles: Abelianisation and q q -deformed Yang-Mills theory,” J. High Energy Phys. 0605
2006
Later among the works it cites.
X. Arsiwalla, R. Boels, M. Marino and A. Sinkovics, “Phase transitions in q-deformed 2d Yang-Mills theory and topological strings,” Phys. Rev. D 73
2006
Later among the works it cites.
N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara and R. J. Szabo, “Topological strings and large N N phase transitions. I: Nonchiral expansion of q q -deformed Yang-Mills theory,” J. High Energy Phys. 0601
2006
Later among the works it cites.
M. Aganagic, A. Neitzke and C. Vafa, “BPS microstates and the open topological string wave function,” Adv. Theor. Math. Phys. 10 603–656 (2006) [arXiv:hep-th/0504054]
2006
Later among the works it cites.
Y. Dolivet and M. Tierz, “Chern-Simons matrix models and Stieltjes-Wigert polynomials,” J. Math. Phys. 48
2007
Later among the works it cites.
F. van de Bult, ”Hyperbolic Hypergeometric Functions,” , PhD Thesis, University of Amsterdam (2007)
2007
Later among the works it cites.
2008
Later among the works it cites.
A. Yu. Morozov, “Unitary integrals and related matrix models,” Theor. Math. Phys. 162
2010
Later among the works it cites.
2010
Later among the works it cites.
S. Giombi, V. Pestun and R. Ricci, “Notes on supersymmetric Wilson loops on a two-sphere,” JHEP 1007
2010
Later among the works it cites.