Fetching the paper…

Reading the bibliography…

2013

Lax matrix solution of c=1 Conformal Field Theory

Eynard, Bertrand, Ribault, Sylvain

Original
PDF
Post on X

Understand

To a correlation function in a two-dimensional conformal field theory with the central charge $c=1$, we associate a matrix differential equation $\Psi' = L \Psi$, where the Lax matrix $L$ is a matrix square root of the energy-momentum tensor.

Then local conformal symmetry implies that the differential equation is isomonodromic.
This provides a justification for the recently observed relation between four-point conformal blocks and solutions of the Painlev\'e VI equation.
This also provides a direct way to compute the three-point function of Runkel-Watts theory -- the common $c\rightarrow 1$ limit of Minimal Models and Liouville theory.

Lax matrix solution of c=1 Conformal Field Theory · Around

Built on

P. Bouwknegt, K. Schoutens (1993 review) W symmetry in conformal field theory
1993
Earlier work this paper cites.
V. V. Bazhanov, S. L. Lukyanov, A. B. Zamolodchikov (1996) Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
1996
Earlier work this paper cites.
A. B. Zamolodchikov, A. B. Zamolodchikov (1996) Structure constants and conformal bootstrap in Liouville field theory
1996
Earlier work this paper cites.
I. Runkel, G. M. T. Watts (2001) A non-rational CFT with c = 1 as a limit of minimal models
2001
Earlier work this paper cites.

Similar

V. Schomerus (2003) Rolling tachyons from Liouville theory
2003
Cited alongside, same era.
A. Bytsko, J. Teschner (2009) The integrable structure of nonrational conformal field theory
Original
2009
Cited alongside, same era.
M. Bergere, B. Eynard (2009) Determinantal formulae and loop equations
Original
2009
Cited alongside, same era.
L. F. Alday, D. Gaiotto, Y. Tachikawa (2010) Liouville Correlation Functions from Four-dimensional Gauge Theories
Original
2010
Cited alongside, same era.

Then

O. Gamayun, N. Iorgov, O. Lisovyy (2012) Conformal field theory of Painlevé VI
Original
2012
Later among the works it cites.
L. Chekhov, B. Eynard, S. Ribault (2013) Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Original
2013
Closest in time.
N. Iorgov, O. Lisovyy, Y. Tykhyy (2013) Painlevé VI connection problem and monodromy of c=1 conformal blocks
Original
2013
Closest in time.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…