Fetching the paper…

Reading the bibliography…

2021

Whittaker vectors for $\mathcal{W}$-algebras from topological recursion

Borot, Gaëtan, Bouchard, Vincent, Chidambaram, Nitin Kumar et al.

Original
PDF
Post on X

Understand

We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures.

This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of $G$-bundles over $\mathbb{P}^2$ for $G$ a complex simple Lie group, can be computed by a non-commutative version of the Chekhov-Eynard-Orantin topological recursion.
We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level).
On the physics side, it means that the Nekrasov partition function for pure $\mathcal{N} = 2$ four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods.

Whittaker vectors for $\mathcal{W}$-algebras from topological recursion · Around

Built on

Argyres–Douglas theories and Liouville irregular states
Original
T. Nishinaka and T. Uetoko · 1905
Earlier work this paper cites.
From the quantum geometry of Fuchsian systems to conformal blocks of W W -algebras
Original
R. Belliard and B. Eynard · 1907
Earlier work this paper cites.
Super quantum airy structures
Original
V. Bouchard, P. Ciosmak, L. Hadasz, K. Osuga, B. Ruba, and P. Sułkowski · 1907
Earlier work this paper cites.
Hilbert schemes of nonreduced divisors in Calabi–Yau threefolds and W W -algebras
Original
W. Chuang, T. Creutzig, D.-E. Diaconescu, and Y. Soibelman · 1907
Earlier work this paper cites.
From topological recursion to wave functions and PDEs quantizing hyperelliptic curves
Original
B. Eynard and E. Garcia-Failde · 1911
Earlier work this paper cites.
Quantization of hyperelliptic curves from isomonodromic systems and topological recursion
Original
O. Marchal and N. Orantin · 1911
Earlier work this paper cites.
Higher genus correlators from the hermitian 1-matrix model
J. Ambjørn, L.O. Chekhov, and Yu. Makeenko · 1992
Earlier work this paper cites.
Affine Kac–Moody algebras at the critical level and Gelfand–Dikii algebras
B. Feigin and E. Frenkel · 1992
Earlier work this paper cites.
Modular invariance of characters of vertex operator algebras
Y. Zhu · 1996
Earlier work this paper cites.
Seiberg–Witten theory and integrable systems
A. Marshakov · 1999
Earlier work this paper cites.
All genus correlation functions for the hermitian 1 1 -matrix model
B. Eynard · 2004
Earlier work this paper cites.
Quantum reduction and representation theory of superconformal algebras
V.G. Kac and M. Wakimoto · 2004
Earlier work this paper cites.
Vertex algebras and vertex Poisson algebras
H. Li · 2004
Earlier work this paper cites.
Duality of subregular W W -algebras and principal W W -superalgebras
Original
T. Creutzig, N. Genra, and S. Nakatsuka · 2005
Earlier work this paper cites.
Trialities of w w -algebras
Original
T: Creutzig and A.R. Linshaw · 2005
Earlier work this paper cites.
Conformal field theories associated to regular chiral vertex operator algebras. I. Theories over the projective line
K. Nagatomo and A. Tsuchiya · 2005
Earlier work this paper cites.
Instanton counting on blowup. 1
H. Nakajima and K. Yoshioka · 2005
Earlier work this paper cites.
Matrix eigenvalue model: Feynman graph technique for all genera
L.O. Chekhov and B. Eynard · 2006
Earlier work this paper cites.
Representation theory of W W -algebras
T. Arakawa · 2007
Earlier work this paper cites.
𝒩 = 1 \mathcal{N}=1 super topological recursion
Original
V. Bouchard and K. Osuga · 2007
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Weil–Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models
Original
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Topological expansion of mixed correlations in the hermitian 2 2 matrix model and x − y x-y symmetry of the F g F_{g} invariants
Original
B. Eynard and N. Orantin · 2008
Earlier work this paper cites.
Remodeling the B-model
Original
V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti · 2009
Earlier work this paper cites.
A new class of higher quantum Airy structures as modules of W ⁡ ( 𝔤 𝔩 r ) W(\mathfrak{gl}_{r}) -algebras
Original
V. Bouchard and K. Mastel · 2009
Earlier work this paper cites.
Topological expansion of the Bethe ansatz, and quantum algebraic geometry
Original
L.O. Chekhov, B. Eynard, and O. Marchal · 2009
Earlier work this paper cites.
Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
Original
B. Eynard and O. Marchal · 2009
Earlier work this paper cites.
Geometrical interpretation of the topological recursion, and integrable string theories
Original
B. Eynard and N. Orantin · 2009
Earlier work this paper cites.
Topological recursion in random matrices and enumerative geometry
Original
B. Eynard and N. Orantin · 2009
Earlier work this paper cites.
Liouville correlation functions from four-dimensional gauge theories
Original
L.F. Alday, D. Gaiotto, and Y. Tachikawa · 2010
Earlier work this paper cites.
Urod algebras and translation of W W -algebras
Original
T. Arakawa, T. Creutzig, and B. Feigin · 2010
Earlier work this paper cites.

Similar

Higher Airy structures and topological recursion on singular spectral curves
Original
G. Borot, R. Kramer, and Y. Schüler · 2010
Cited alongside, same era.
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Original
L.O. Chekhov, B. Eynard, and O. Marchal · 2011
Cited alongside, same era.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Original
R. Dijkgraaf, H. Fuji, and M. Manabe · 2011
Cited alongside, same era.
Loop equations and topological recursion for the arbitrary- β \beta two-matrix model
Original
M. Bergère, B. Eynard, O. Marchal, and A. Prats-Ferrer · 2012
Cited alongside, same era.
Wild quiver gauge theories

Then

Geometric recursion
Original
J.E. Andersen, G. Borot, and N. Orantin · 2017
Later among the works it cites.
Introduction to W W -algebras and their representation theory
Original
T. Arakawa · 2017
Later among the works it cites.
Integrable differential systems of topological type and reconstruction by the topological recursion
Original
R. Belliard, B. Eynard, and O. Marchal · 2017
Later among the works it cites.
Spectral curves, root systems, and application to SU ⁡ ( N ) \mathrm{SU}(N) Chern–Simons theory on Seifert spaces
Original
G. Borot and B. Eynard · 2017
Later among the works it cites.
Reconstructing WKB from topological recursion
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

G. Bonelli, K. Maruyoshi, and A. Tanzini · 2012

Cited alongside, same era.

Geometry of spectral curves and all order dispersive integrable system

G. Borot and B. Eynard · 2012

Cited alongside, same era.

Topological recursion for Kadomtsev–Petviashvili tau functions of hypergeometric type

B. Bychkov, P. Dunin-Barkowski, M. Kazarian, and S. Shadrin · 2012

Cited alongside, same era.

Irregular singularities in Liouville theory and Argyres–Douglas type gauge theories, I

D. Gaiotto and J. Teschner · 2012

Cited alongside, same era.

The ABCDEFG of instantons and W W -algebras

C.A. Keller, N. Mekareeya, J. Song, and Y. Tachikawa · 2012

Cited alongside, same era.

The ABCDEFG of instantons and W-algebras

C.A. Keller, N. Mekareeya, J. Song, and Y. Tachikawa · 2012

Cited alongside, same era.

W W -constraints for the total descendant potential of a simple singularity

B. Bakalov and T. Milanov · 2013

Cited alongside, same era.

Think globally, compute locally

V. Bouchard and B. Eynard · 2013

Cited alongside, same era.

V. Bouchard and B. Eynard · 2017

Later among the works it cites.

Screening operators for W W -algebras

N. Genra · 2017

Later among the works it cites.

Moduli spaces of curves and enumerative geometry via topological recursion

D. Lewański · 2017

Later among the works it cites.

Weighted Hurwitz numbers and topological recursion: an overview

A. Alexandrov, G. Chapuy, B. Eynard, and J. Harnad · 2018

Later among the works it cites.

Integrability of W ⁡ ( 𝔰 𝔩 d ) W(\mathfrak{sl}_{d}) -symmetric toda conformal field theories

R. Belliard and B. Eynard · 2018

Later among the works it cites.

Higher Airy structures, W W -algebras and topological recursion

G. Borot, V. Bouchard, N.K. Chidambaram, T. Creutzig, and D. Noshchenko · 2018

Later among the works it cites.

Chern–Simons theory on spherical seifert manifolds, topological strings and integrable systems

G. Borot and A. Brini · 2018

Later among the works it cites.

Topological recursion on the Bessel curve

N. Do and P. Norbury · 2018

Later among the works it cites.

Painlevé equations, topological type property and reconstruction by the topological recursion

K. Iwaki, O. Marchal, and A. Saenz · 2018

Later among the works it cites.

Airy structures and symplectic geometry of topological recursion

M. Kontsevich and Y. Soibelman · 2018

Later among the works it cites.

Quantization of spectral curves for meromorphic Higgs bundles through topological recursion

M. Mulase and O. Dumitrescu · 2018

Later among the works it cites.

W W -algebras as coset vertex algebras

T. Arakawa, T. Creutzig, and A.R. Linshaw · 2019

Later among the works it cites.

Cosets of affine vertex algebras inside larger structures

T. Creutzig and A.R. Linshaw · 2019

Later among the works it cites.

Vertex algebras at the corner

D. Gaiotto and M. Rapčák · 2019

Later among the works it cites.

Universal two-parameter even spin W ∞ W_{\infty} -algebra

S. Kanade and A.R. Linshaw · 2019

Later among the works it cites.

Quantum groups and quantum cohomology

D. Maulik and A. Okounkov · 2019

Later among the works it cites.

Cohomological Hall algebras, vertex algebras and instantons

M. Rapčák, Y. Soibelman, Y. Yang, and G. Zhao · 2019

Later among the works it cites.

Topological recursion and geometry

G. Borot · 2020

Later among the works it cites.

On the remodeling conjecture for toric Calabi–Yau 3 3 -orbifolds

B. Fang, C.-C. Liu, and Z. Zong · 2020

Later among the works it cites.

VOA[ M 4 M_{4} ]

B. Feigin and S. Gukov · 2020

Later among the works it cites.

A new spin on Hurwitz theory and ELSV via theta characteristics

A. Giacchetto, R. Kramer, and D. Lewański · 2021

Closest in time.

Universal two-parameter W ∞ W_{\infty} -algebra and vertex algebras of type W ⁡ ( 2 , 3 , … , N ) W(2,3,\ldots,N)

A.R. Linshaw · 2021

Closest in time.

Trialities of orthosymplectic W W -algebras

T. Creutzig and A.R. Linshaw · 2022

Closest in time.

Super topological recursion and Gaiotto vectors for superconformal blocks

K. Osuga · 2022

Closest in time.

A new cohomology class on the moduli space of curves

P. Norbury · 2023

Closest in time.

CFT and topological recursion

I. Kostov and N. Orantin · 2028

Closest in time.