Built on

P. Saad, S. H. Shenker and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115
Original
1903
Earlier work this paper cites.
B. Ruba, “Analyticity of the free energy for quantum Airy structures,” J. Phys. A 53
Original
1906
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363
Original
1907
Earlier work this paper cites.
K. Osuga, “Topological Recursion in the Ramond Sector,” JHEP 10
Original
1909
Earlier work this paper cites.
L. Hadasz and B. Ruba, “Airy structures for semisimple Lie algebras,” arXiv:1911.10453
Original
1911
Earlier work this paper cites.
K. Barron and N. Vander Werf, “On permutation-twisted free fermions and two conjectures,” J. Phys. Conf. Ser. 474
Original
1958
Earlier work this paper cites.
V. G. Kac, “A sketch of Lie superalgebra theory,” Commun. Math. Phys. 53 (1977)
1977
Earlier work this paper cites.
E. Brézin and D. Gross, “The external field problem in the large N N limit of QCD,” Phys. Lett. B
1980
Earlier work this paper cites.
D. J. Gross and E. Witten, “Possible Third Order Phase Transition in the Large N Lattice Gauge Theory,” Phys. Rev. D 21
1980
Earlier work this paper cites.
D. B. Fuks, “Cohomology of Infinite-Dimensional Lie Algebras,” Monographs in Contemporary Mathematics , Springer US,1986
1986
Earlier work this paper cites.
E. Witten, “Two-dimensional gravity and intersection theory on moduli space,” Surveys in differential geometry (Cambridge, MA, 1990), 1, Bethlehem, PA: Lehigh Univ., pp. 243–310
1990
Earlier work this paper cites.
R. Dijkgraaf, E. Verlinde and H. Verlinde, “Loop equations and Virasoro constraints in nonperturbative 2D quantum gravity,” Nucl. Phys. B348 (1991) 435–456
1991
Earlier work this paper cites.
L. Alvarez-Gaume, H. Itoyama, J. L. Manes and A. Zadra, “Superloop equations and two-dimensional supergravity,” Int. J. Mod. Phys. A 7
1992
Earlier work this paper cites.
M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Commun. Math. Phys. 147
1992
Earlier work this paper cites.
K. Becker and M. Becker, “Nonperturbative solution of the superVirasoro constraints,” Mod. Phys. Lett. A 8
1993
Earlier work this paper cites.
V. Kac and W. q. Wang, “Vertex operator superalgebras and their representations,” in Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups , volume 175 of Contemporary Mathematics , AMS, 1994 [ arXiv:hep-th/9312065 ]
1994
Earlier work this paper cites.
H. Li, “Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules,” Journal of Pure and Applied Algebra, Volume 109, Issue 2, pp. 143-195 (1996) [ arXiv:q-alg/9504022 ]
1996
Earlier work this paper cites.

Similar

A. Mironov, A. Morozov and G. W. Semenoff, “Unitary matrix integrals in the framework of generalized Kontsevich model. 1. Brezin-Gross-Witten model,” Int. J. Mod. Phys. A 11
1996
Cited alongside, same era.
D. Ben-Zvi and E. Frenkel, “Vertex Algebras and Algebraic Curves,” Mathematical Surveys and Monographs , Volume: 88 (2004), 400p
2004
Cited alongside, same era.
R. M. Kaufmann, “Second Quantized Frobenius Algebras”, Commun. Math. Phys. 248
2004
Cited alongside, same era.
L.O. Chekhov and B. Eynard, “Matrix eigenvalue model: Feynman graph technique for all genera,” JHEP 0612:026, 2006 [ arXiv:math-ph/0604014 ]
2006
Cited alongside, same era.
V. Bouchard and K. Osuga, “ 𝒩 = 1 \mathcal{N}=1 Super Topological Recursion,” arXiv:2007.13186
Original
2007
Cited alongside, same era.

Then

B. Eynard “Invariants of spectral curves and intersection theory of moduli spaces of complex curves,” Commun. Number Theory and Physics
Original
2014
Later among the works it cites.
G. Borot and B. Eynard, “All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials,” Quantum Topology, Volume 6, Issue 1, pp. 39-138 (2015) [ arXiv:1205.2261 ]
Original
2015
Later among the works it cites.
B. Eynard and N. Orantin, “Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture,” Comm. Math. Phys. 337
Original
2015
Later among the works it cites.
B. Fang, C.-C. M. Liu, and Z. Zong, “All genus open-closed mirror symmetry for affine toric Calabi-Yau 3-orbifolds,” in Proceedings of Symposia in Pure Mathematics
Original
2015
Later among the works it cites.

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2019

Super Quantum Airy Structures

Bouchard, Vincent, Ciosmak, Paweł, Hadasz, Leszek et al.

Understand

We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures.

We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion.
We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations.
Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional -- which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss -- as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

Built on

P. Saad, S. H. Shenker and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115
Original
1903
Earlier work this paper cites.
B. Ruba, “Analyticity of the free energy for quantum Airy structures,” J. Phys. A 53
Original
1906
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363
Original
1907
Earlier work this paper cites.
K. Osuga, “Topological Recursion in the Ramond Sector,” JHEP 10
Original
1909
Earlier work this paper cites.
L. Hadasz and B. Ruba, “Airy structures for semisimple Lie algebras,” arXiv:1911.10453
Original
1911
Earlier work this paper cites.
K. Barron and N. Vander Werf, “On permutation-twisted free fermions and two conjectures,” J. Phys. Conf. Ser. 474
Original
1958
Earlier work this paper cites.
V. G. Kac, “A sketch of Lie superalgebra theory,” Commun. Math. Phys. 53 (1977)
1977
Earlier work this paper cites.
E. Brézin and D. Gross, “The external field problem in the large N N limit of QCD,” Phys. Lett. B
1980
Earlier work this paper cites.
D. J. Gross and E. Witten, “Possible Third Order Phase Transition in the Large N Lattice Gauge Theory,” Phys. Rev. D 21
1980
Earlier work this paper cites.
D. B. Fuks, “Cohomology of Infinite-Dimensional Lie Algebras,” Monographs in Contemporary Mathematics , Springer US,1986
1986
Earlier work this paper cites.
E. Witten, “Two-dimensional gravity and intersection theory on moduli space,” Surveys in differential geometry (Cambridge, MA, 1990), 1, Bethlehem, PA: Lehigh Univ., pp. 243–310
1990
Earlier work this paper cites.
R. Dijkgraaf, E. Verlinde and H. Verlinde, “Loop equations and Virasoro constraints in nonperturbative 2D quantum gravity,” Nucl. Phys. B348 (1991) 435–456
1991
Earlier work this paper cites.
L. Alvarez-Gaume, H. Itoyama, J. L. Manes and A. Zadra, “Superloop equations and two-dimensional supergravity,” Int. J. Mod. Phys. A 7
1992
Earlier work this paper cites.
M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Commun. Math. Phys. 147
1992
Earlier work this paper cites.
K. Becker and M. Becker, “Nonperturbative solution of the superVirasoro constraints,” Mod. Phys. Lett. A 8
1993
Earlier work this paper cites.
V. Kac and W. q. Wang, “Vertex operator superalgebras and their representations,” in Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups , volume 175 of Contemporary Mathematics , AMS, 1994 [ arXiv:hep-th/9312065 ]
1994
Earlier work this paper cites.
H. Li, “Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules,” Journal of Pure and Applied Algebra, Volume 109, Issue 2, pp. 143-195 (1996) [ arXiv:q-alg/9504022 ]
1996
Earlier work this paper cites.

Similar

A. Mironov, A. Morozov and G. W. Semenoff, “Unitary matrix integrals in the framework of generalized Kontsevich model. 1. Brezin-Gross-Witten model,” Int. J. Mod. Phys. A 11
1996
Cited alongside, same era.
D. Ben-Zvi and E. Frenkel, “Vertex Algebras and Algebraic Curves,” Mathematical Surveys and Monographs , Volume: 88 (2004), 400p
2004
Cited alongside, same era.
R. M. Kaufmann, “Second Quantized Frobenius Algebras”, Commun. Math. Phys. 248
2004
Cited alongside, same era.
L.O. Chekhov and B. Eynard, “Matrix eigenvalue model: Feynman graph technique for all genera,” JHEP 0612:026, 2006 [ arXiv:math-ph/0604014 ]
2006
Cited alongside, same era.
V. Bouchard and K. Osuga, “ 𝒩 = 1 \mathcal{N}=1 Super Topological Recursion,” arXiv:2007.13186
Original
2007
Cited alongside, same era.

Then

B. Eynard “Invariants of spectral curves and intersection theory of moduli spaces of complex curves,” Commun. Number Theory and Physics
Original
2014
Later among the works it cites.
G. Borot and B. Eynard, “All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials,” Quantum Topology, Volume 6, Issue 1, pp. 39-138 (2015) [ arXiv:1205.2261 ]
Original
2015
Later among the works it cites.
B. Eynard and N. Orantin, “Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture,” Comm. Math. Phys. 337
Original
2015
Later among the works it cites.
B. Fang, C.-C. M. Liu, and Z. Zong, “All genus open-closed mirror symmetry for affine toric Calabi-Yau 3-orbifolds,” in Proceedings of Symposia in Pure Mathematics
Original
2015
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

B. Eynard and N. Orantin. “Invariants of algebraic curves and topological expansion,” Commun. Number Theory Phys., 1(2):347–452 (2007) [ arXiv:math-ph/0702045 ]

2007

Cited alongside, same era.

M. Mirzakhani, “Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces,” Invent. Math. 167, 179–222 (2007)

2007

Cited alongside, same era.

V. Bouchard and M. Marino, “Hurwitz numbers, matrix models and enumerative geometry,” Proc. Symp. Pure Math. 78

Original

2008

Cited alongside, same era.

V. Bouchard, A. Klemm, M. Marino and S. Pasquetti, “Remodeling the B-model,” Commun. Math. Phys. 287

Original

2009