Fetching the paper…

Reading the bibliography…

2016

Q-deformed Painleve tau function and q-deformed conformal blocks

Bershtein, M. A., Shchechkin, A. I.

Original
PDF
Post on X

Understand

We propose $q$-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev\'e $\tau$ function.

Namely we propose formula for $\tau$ function for $q$-difference Painlev\'e equation corresponding to $A_7^{(1)}{}'$ surface (and $A_1^{(1)}$ symmetry) in Sakai's classification.
In this formula $\tau$ function equals the series of $q$-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure $SU(2)$ 5d theory).

Q-deformed Painleve tau function and q-deformed conformal blocks · Around

Built on

K. Okamoto, Sur les feuilletages associés aux équations du second ordre a points critiques fixés de P. Painlevé
1979
Earlier work this paper cites.
N. Seiberg, Five dimensional SUSY field theories, non-trivial fixed points and string dynamics
1996
Earlier work this paper cites.
G. Andrews, R. Askey, R. Roy, Special functions
1999
Earlier work this paper cites.
A. Ramani, B. Grammaticos, T. Tamizhmani, Quadratic relations in continuous and discrete Painleve equations
2000
Earlier work this paper cites.
H. Sakai, Rational surfaces associated with affine root systems and geometry of the Painlevé equations
2001
Earlier work this paper cites.
B. Grammaticos, T. Tamizhmani, A. Ramani, A. S. Carstea, K.M.Tamizhmani, A bilinear approach to the discrete Painleve I equations
2002
Earlier work this paper cites.
T. Eguchi, H. Kanno, Topological strings and Nekrasov’s formulas
2003
Earlier work this paper cites.
A. Iqbal, A. K. Kashani-Poor, S U ( N ) SU(N) geometries and topological string amplitudes,
2006
Earlier work this paper cites.

Similar

Y. Ohyama, H. Kawamuko, H. Sakai, K. Okamoto, Studies on the Painlevé Equations, V, Third Painlevé Equations of Special Type PIII(D 7 ) and PIII(D 8 ) ,J. Math. Sci. Univ. Tokyo 13
2006
Cited alongside, same era.
T. Tsuda, Tau Functions of q-Painlevé III and IV Equations
2006
Cited alongside, same era.
H. Sakai, Problem: Discrete Painlevé equations and their Lax forms
2007
Cited alongside, same era.
H. Awata, Y. Yamada, Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
Original
2010
Cited alongside, same era.
V. Belavin, B. Feigin, Super Liouville conformal blocks from 𝒩 = 2 \mathcal{N}=2 S U ( 2 ) SU(2) quiver gauge theories
Original
2011
Cited alongside, same era.

Then

O. Gamayun, N. Iorgov, O. Lisovyy, How instanton combinatorics solves Painlevé VI,V and III’s
Original
2013
Later among the works it cites.
Y. Ito, K. Maruyoshi, T. Okuda, Scheme dependence of instanton counting in ALE spaces
Original
2013
Later among the works it cites.
V. Spiridonov, Elliptic hypergeometric functions
Original
2013
Later among the works it cites.
M. Bershtein, A. Shchechkin, Bilinear equations on Painlevé tau functions from CFT
Original
2015
Later among the works it cites.
N.Iorgov, O.Lisovyy, J.Teschner, Isomonodromic τ \tau functions from Liouville conformal blocks , Commun. Math.Phys. 336(2)
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, Instantons on ALE spaces and Super Liouville Conformal Field Theories

2011

Cited alongside, same era.

O. Gamayun, N. Iorgov, O. Lisovyy, Conformal field theory of Painlevé VI

2012

Cited alongside, same era.

A. Belavin, M. Bershtein, B. Feigin, A. Litvinov, G. Tarnopolsky, Instanton moduli spaces and bases in coset conformal field theory

2013

Cited alongside, same era.

M. Bershtein, A. Shchechkin, Bäcklund transformation of Painlevé III( D 8 D_{8} ) tau function

Cited in the paper.

G. Bonelli, A. Grassi, A. Tanzini, Seiberg-Witten theory as a Fermi gas

Cited in the paper.

G. Bonelli, A. Grassi, A. Tanzini, to appear

Cited in the paper.

K. Kajiwara, M. Noumi, Y. Yamada, Geometric Aspects of Painlevé Equations

Cited in the paper.

2015

Later among the works it cites.

A. Its, O. Lisovyy, Yu. Tykhyy, Connection problem for the sine-Gordon/Painlevé III tau function and irregular conformal blocks IMRN (2015) 18

2015

Later among the works it cites.

H, Nakajima, K. Yoshioka, Instanton counting on blowup. II. K K -theoretic partition function

2015

Later among the works it cites.

B. Grammaticos, A. Ramani, Parameterless discrete Painleve equations and their Miura relations

2016

Closest in time.