Affine SL(2) Conformal Blocks from 4d Gauge Theories

Luis F. Alday1, Yuji Tachikawa1
1School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA

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Tài liệu tham khảo

Gaiotto, D.: $${{\mathcal{N}} =2}$$ Dualities. arXiv:0904.2715 [hep-th]

Alday L.F., Gaiotto D., Tachikawa Y.: Liouville correlation functions from four-dimensional gauge theories. Lett. Math. Phys. 91, 167–197 (2010) arXiv:0906.3219 [hep-th]

Nekrasov N.A.: Seiberg–Witten prepotential from instanton counting. Adv. Theor. Math. Phys. 7, 831–864 (2004) arXiv:hep-th/0206161

Wyllard N.: A N–1 Conformal Toda field theory correlation functions from conformal $${{\mathcal{N}} =2SU(N)}$$ quiver gauge theories. JHEP 11, 002 (2009) arXiv:0907.2189 [hep-th]

Mironov A., Morozov A.: On AGT relation in the case of U(3). Nucl. Phys. B 825, 1–37 (2010) arXiv:0908.2569 [hep-th]

Alday L.F., Gaiotto D., Gukov S., Tachikawa Y., Verlinde H.: Loop and surface operators in $${{\mathcal{N}} =2}$$ gauge theory and Liouville modular geometry. JHEP 01, 113 (2010) arXiv:0909.0945 [hep-th]

Kozcaz, C., Pasquetti, S., Wyllard, N.: A & B model approaches to surface operators and Toda theories. arXiv:1004.2025 [hep-th]

Drukker N., Morrison D.R., Okuda T.: Loop operators and S-duality from curves on Riemann surfaces. JHEP 09, 031 (2009) arXiv:0907.2593 [hep-th]

Drukker N., Gomis J., Okuda T., Teschner J.: Gauge theory loop operators and Liouville theory. JHEP 02, 057 (2010) arXiv:0909.1105 [hep-th]

Drukker, N., Gaiotto, D., Gomis, J.: The virtue of defects in 4D gauge theories and 2D CFTs. arXiv:1003.1112 [hep-th]

Gukov, S., Witten, E.: Gauge theory, ramification, and the geometric Langlands program. arXiv:hep-th/0612073

Braverman A.: Instanton counting via affine Lie algebras. I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors. In: Hurturbise, J., Markman, E. (eds) Workshop on algebraic structures and Moduli Spaces: CRM Workshop, AMS, Providence (2003) arXiv:math/0401409

Braverman A., Etingof P.: Instanton counting via affine Lie algebras. II. From Whittaker vectors to the Seiberg–Witten prepotential. In: Bernstein, J., Hinich, V., Melnikov, A. (eds) Studies in Lie Theory: dedicated to A. Joseph on his 60th birthday, Birkhäuser, Boston (2006) arXiv:math/0409441

Negut A.: Laumon spaces and the Calogero-Sutherland integrable system. Invent. Math. 178, 299 (2008) arXiv:0811.4454 [math.AG]

Feigin, B., Finkelberg, M., Negut, A., Rybnikov, L.: “Yangians and cohomology rings of Laumon spaces,” arXiv:0812.4656 [math.AG]

Nekrasov, N.A., Shatashvili, S.L.: Quantization of integrable systems and four dimensional gauge theories. arXiv:0908.4052 [hep-th]

Teschner, J.: Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence. arXiv:1005.2846 [hep-th]

Flume R., Poghossian R.: An algorithm for the microscopic evaluation of the coefficients of the Seiberg–Witten prepotential. Int. J. Mod. Phys. A 18, 2541 (2003) arXiv:hep-th/0208176

Nakajima H., Yoshioka K.: Instanton counting on blowup, I. Invent. Math. 162, 313 (2005) arXiv:math/0306198

Fucito F., Morales J.F., Poghossian R.: Instantons on quivers and orientifolds. JHEP 10, 037 (2004) arXiv:hep-th/0408090

Nakajima H., Yoshioka K.: Lectures on instanton counting. In: Hurturbise, J., Markman, E. (eds) Workshop on Algebraic Structures and Moduli Spaces: CRM Workshop, AMS, Providence (2003) arXiv:math/0311058

Carlsson, E., Okounkov, A.: Ext and vertex operators. arXiv:0801.2565 [math.AG]

Gukov, S.: Surface operators and knot homologies. arXiv:0706.2369 [hep-th]

Tan, M.-C.: Integration over the u-plane in Donaldson theory with surface operators. arXiv:0912.4261 [hep-th]

Gaiotto, D.: Surface operators in $${{\mathcal{N}} =2}$$ 4D gauge theories. arXiv:0911.1316 [hep-th]

Kronheimer P.B., Mrowka T.S.: Gauge theory for embedded surfaces, I. Topology 32, 773 (1993)

Kronheimer P.B., Mrowka T.S.: Gauge theory for embedded surfaces, II. Topology 34, 37 (1995)

Biquard O.: Sur les Fibrés Paraboliques sur une Surface Complexe. J. London Math. Soc. 53, 302 (1996)

Martinec E.J., Warner N.P.: Integrable Systems and Supersymmetric Gauge Theory. Nucl. Phys. B 459, 97–112 (1996) arXiv:hep-th/9509161

Donagi R., Witten E.: Supersymmetric Yang-Mills Theory and Integrable Systems. Nucl. Phys. B 460, 299–334 (1996) arXiv:hep-th/9510101

Itoyama H., Morozov A.: Integrability and Seiberg-Witten Theory: Curves and Periods. Nucl. Phys. B 477, 855–877 (1996) arXiv:hep-th/9511126

Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser system from two-dimensional current algebra. arXiv:hep-th/9401021

Beilinson, A., Drinfeld, V.: Quantization of Hitchin’s integrable system and Hecke Eigensheaves. c2000. http://www.math.utexas.edu/users/benzvi/BD/hitchin.pdf

Frenkel E.: Lectures on the Langlands program and conformal field theory. In: Cartier, P.E., Julia, B., Moussa, P., Vanhove, P. (eds) Frontiers in Number Theory, Physics and Geometry II, Springer, Berlin (2007) arXiv:hep-th/0512172

Knizhnik V.G., Zamolodchikov A.B.: Current algebra and Wess–Zumino model in two dimensions. Nucl. Phys. B 247, 83–103 (1984)

Bernard D.: On the Wess–Zumino–Witten models on the Torus. Nucl. Phys. B 303, 77 (1988)

Etingof P.I., Kirillov A.A. Jr.: Representation of affine Lie algebras, parabolic differential equations and Lamé functions. Duke Math. J. 74, 585 (1994) arXiv:hep-th/9310083

Felder G., Weiczerkowski C.: Conformal blocks on elliptic curves and the Knizhnik–Zamolodchikov–Bernard equations. Commun. Math. Phys. 176, 133–162 (1996) arXiv:hep-th/9411004

Martinec E.J.: Integrable structures in supersymmetric gauge and string theory. Phys. Lett. B 367, 91–96 (1996) arXiv:hep-th/9510204

Bonelli, G., Tanzini, A.: Hitchin systems, $${{\mathcal{N}} =2}$$ gauge theories and W-gravity. arXiv:0909.4031 [hep-th]

Ribault S., Teschner J.: $${{\rm H}^+_3}$$ WZNW correlators from Liouville theory. JHEP 06, 014 (2005) arXiv:hep-th/0502048

Reshetikhin, N., Varchenko, A.: Quasiclassical asymptotics of solutions to the KZ equations. arXiv:hep-th/9402126

Nekrasov, N., Witten, E.: The omega deformation, branes, integrability, and Liouville theory. arXiv:1002.0888 [hep-th]

Bershadsky M., Ooguri H.: Hidden SL(N) symmetry in conformal field theories. Commun. Math. Phys. 126, 49 (1989)

Feigin B., Frenkel E.: Quantization of the Drinfeld–Sokolov reduction. Phys. Lett. B 246, 75–81 (1990)

Ribault S.: On SL(3) Knizhnik–Zamolodchikov equations and W 3 null-vector equations. JHEP 10, 002 (2009) arXiv:0811.4587 [hep-th]

Giribet, G.: On Triality in $${{\mathcal{N}} =2}$$ SCFT with N F  = 4. arXiv:0912.1930 [hep-th]

Hikida Y., Schomerus V.: $${{\rm H}^+_3}$$ WZNW Model from Liouville Field Theory. JHEP 10, 064 (2007) arXiv:0706.1030 [hep-th]

Giribet G., Nakayama Y., Nicolás L.: Langlands duality in Liouville- $${{\rm H}_3^+}$$ WZNW correspondence. Int. J. Mod. Phys. A 24, 3137–3170 (2009) arXiv:0805.1254 [hep-th]

Pestun, V.: Localization of Gauge theory on a four-sphere and supersymmetric Wilson loops. arXiv:0712.2824 [hep-th]

Awata H., Yamada Y.: Fusion rules for the fractional level SL(2) algebra. Mod. Phys. Lett. A 7, 1185–1196 (1992)