The Euler anomaly and scale factors in Liouville/Toda CFTs
arXiv:1310.5033 · doi:10.1007/JHEP04(2014)127
Abstract
The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class and two dimensional nonrational CFTs is clarified. On the two dimensional side, this involves a careful treatment of scale factors in Liouville/Toda correlators. Using ideas from tinkertoy constructions for Gaiotto duality, a framework is proposed for evaluating these scale factors. The representation theory of Weyl groups plays a critical role in this framework.
55 pages, 16 figures; v2:fixed referencing & typos ; v3: argument about scale factors in Liouville/Toda now phrased in terms of stripped correlators, leading to a sharper conjecture (earlier version had some inaccurate statements). Presentation improved, typos fixed, refs added. I thank the anonymous referee for comments. Version accepted for publication in JHEP
References in corpus (14)
- A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
- S-duality in N=2 supersymmetric gauge theories
- Tinkertoys for Gaiotto Duality
- Exploring Curved Superspace
- Correlation functions in conformal Toda field theory I
- Seiberg-Witten Theories on Ellipsoids
- Correlation functions in conformal Toda field theory II
- H^+_3 WZNW model from Liouville field theory
- Gauge Theory, Ramification, And The Geometric Langlands Program
- M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
- Elliptic Springer Theory
- Supersymmetric Partition Functions and a String Theory in 4 Dimensions
- (de)Tails of Toda CFT
- A review on instanton counting and W-algebras