Abstract
We discuss a relation between the tensor product of the \(\mathcal{N} = 1\) super-Liouville field theory with the imaginary free fermion and a certain projected tensor product of the real and the imaginary Liouville field theories. Using techniques of two dimensional, conformal field theory we give a complete proof of their equivalence in the NS sector.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alday, L.F., Gaiotto, D., Tachikawa, Y.: Liouville correlation functions from four-dimensional gauge theories. Lett. Math. Phys. 91, 167 (2010). arXiv:0906.3219 [hep-th]
Belavin, V., Feigin, B.: Super Liouville conformal blocks from N = 2 SU(2) quiver gauge theories. JHEP 1107, 079 (2011). arXiv:1105.5800 [hep-th]
Belavin, A., Mukhametzhanov, B.: N=1 superconformal blocks with Ramond fields from AGT correspondence. JHEP 1301, 178 (2013). arXiv:1210.7454 [hep-th]
Belavin, A., Belavin, V., Bershtein, M.: Instantons and 2d superconformal field theory. JHEP 1109, 117 (2011). arXiv:1106.4001 [hep-th]
Belavin, A.A., Bershtein, M.A., Feigin, B.L., Litvinov, A.V., Tarnopolsky, G.M.: Instanton moduli spaces and bases in coset conformal field theory. Commun. Math. Phys. 319, 269 (2013). arXiv:1111.2803 [hep-th]
Bonelli, G., Maruyoshi, K., Tanzini, A.: Instantons on ALE spaces and super Liouville conformal field theories. JHEP 1108, 056 (2011). arXiv:1106.2505 [hep-th]
Bonelli, G., Maruyoshi, K., Tanzini, A.: Gauge theories on ALE space and super Liouville correlation functions. Lett. Math. Phys. 101, 103 (2012). arXiv:1107.4609 [hep-th]
Crnkovic, C., Sotkov, G.M., Stanishkov, M.: Renormalization group flow for general Su(2) coset models. Phys. Lett. B226, 297 (1989)
Crnkovic, C., Paunov, R., Sotkov, G.M., Stanishkov, M.: Fusions of conformal models. Nucl. Phys. B336, 637 (1990)
Hadasz, L., Jaskolski, Z.: Super-Liouville - double Liouville correspondence. arXiv:1312.4520 [hep-th]
Ito, Y.: Ramond sector of super Liouville theory from instantons on an ALE space. Nucl. Phys. B861, 387 (2012). arXiv:1110.2176 [hep-th]
Lashkevich, M.Y.: Superconformal 2-D minimal models and an unusual coset construction. Mod. Phys. Lett. A8, 851 (1993). arXiv:hep-th/9301093
Lashkevich, M.Y.: Coset construction of minimal models. Int. J. Mod. Phys. A8, 5673–5700 (1993). [hep-th/9304116]
Schomerus, V., Suchanek, P.: Liouville’s imaginary shadow. arXiv:1210.1856 [hep-th]
Wyllard, N.: A N−1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories. JHEP 0911, 002 (2009). arXiv:0907.2189 [hep-th]
Wyllard, N.: Coset conformal blocks and N = 2 gauge theories. arXiv:1109.4264 [hep-th]
Zamolodchikov, A.B.: On the three-point function in minimal Liouville gravity. hep-th/0505063; Zamolodchikov, A.B.: Three-point function in the minimal Liouville gravity. Theor. Math. Phys. 142, 183 (2005)
Acknowledgements
This work was financed by the NCN grant DEC2011/01/B/ST1 /01302.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this paper
Cite this paper
Hadasz, L., Jaskólski, Z. (2014). On the Relation Between an \(\mathcal{N} = 1\) Supersymmetric Liouville Field Theory and a Pair of Non-SUSY Liouville Fields. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_30
Download citation
DOI: https://doi.org/10.1007/978-4-431-55285-7_30
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55284-0
Online ISBN: 978-4-431-55285-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)