Correlation functions in conformal Toda field theory I

By V. Fateev, A. Litvinov. 2007

205 citations recorded by the source corpus.

Two-dimensional sl(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the three-point correlation functions of the exponential fields if one of the three fields has a special form. In this case it is possible to write down and solve explicitly the differential equation for the four-point correlation function if the fourth field is completely degenerate. We give also expressions for the three-point correlation functions in the cases, when they can be expressed in terms of known functions. The semiclassical and minisuperspace approaches in the conformal Toda field theory are studied and the results coming from these approaches are compared with the proposed analytical expression for the three-point correlation function. We show, that in the framework of semiclassical and minisuperspace approaches general three-point correlation function can be reduced to the finite-dimensional integral.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0cbb1c91f7a1d55acc285f05019260c66e8c949e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. F. Benini
2. E. Pomoni
3. Stefano Cremonesi
4. Masato Taki
5. F. Yagi
6. V. Mitev
7. L. Bao
8. N. Wyllard

In Nuclear and High Energy Physics

1. F. Benini
2. Stefano Cremonesi
3. N. Wyllard
4. E. Pomoni
5. F. Yagi
6. V. Mitev
7. L. Bao
8. Masato Taki

In Statistical and Nonlinear Physics

1. N. Wyllard
2. E. Pomoni
3. F. Yagi
4. V. Mitev
5. L. Bao
6. Stefano Cremonesi
7. Masato Taki
8. F. Benini

Citations in the corpus

• Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, methodology): “Next one uses an identity for generalized hypergeometric functions N FN−1 that allows to rewrite the function of x in terms of a sum of N hypergeometric functions of 1/x (see for instance [40]):21 21 We thank Sara Pasquetti for bringing this formula to our attention.”
• Non-Lagrangian theories from brane junctions (2013, methodology): “Furthermore, by generalizing the methods of [81, 82], one should be able to get differential equations, whose solutions should be given by the 3-point functions obtained via our Nekrasov partition functions.”
• A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories (2009, background): “(A.7) In the case when the gauge group is Sp(2N) the Zk’s are determined by Zk = (−1)k 2nn!”
• Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “See [37] for an introduction to the Toda conformal field theory.”