リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「Knizhnik–Zamolodchikov Equations of the Quantum Toroidal gl1 Algebra and Its Quasi-Hopf Twisting」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

Knizhnik–Zamolodchikov Equations of the Quantum Toroidal gl1 Algebra and Its Quasi-Hopf Twisting

CHEEWAPHUTTHISAKUN, Panupong 名古屋大学

2022.11.18

概要

In this thesis, we derive the MacMahon Knizhnik–Zamolodchikov (KZ) equations of quantum toroidal 𝔤𝔩1 algebra 𝑈𝑞1,𝑞2 (𝔤𝔩1) and then solve the equations. Subsequently, motivated by the AGT correspondence, we show how to interpret the solution of the MacMahon KZ equations as a generalization of Nekrasov factor, which is a fundamental quantity in five-dimensional supersymmetric gauge theory. These MacMahon KZ equations and the generalized Nekrasov factor are believed to be related to various objects in quantum field and string theory.

After that, we proceed to investigate the quasi-Hopf twist of quantum toroidal 𝔤𝔩1 algebra 𝑈𝑞1,𝑞2,𝑝(𝔤𝔩1) . We uncover the hidden relation between the quasi-Hopf twisted $ R $-matrix and the elliptic Nekrasov factor, which is considered as a fundamental building block of six-dimensional supersymmetric gauge theory. Then,

we derive KZ equations of 𝑈𝑞1,𝑞2,𝑝(𝔤𝔩1) corresponding to the Fock representation, and show that the solution of the KZ equation can be written in terms of the product of elliptic Nekrasov factors.

参考文献

[1] M. Aganagic, N. Haouzi, C. Kozcaz, and S. Shakirov, Gauge/liouville triality, arXiv:1309.1687

[2] M. Aganagic, N. Haouzi, and S. Shakirov, An-Triality, arXiv:1403.3657

[3] M. Aganagic, and S. Shakirov, Gauge/Vortex duality and AGT, In New dualities of supersymmetric gauge theories, pp. 419-448. Springer, Cham, 2016. arXiv:1412.7132

[4] M. Aganagic, E. Frenkel, and A. Okounkov, Quantum q-Langlands correspondence, Transactions of the Moscow Mathematical Society 79 (2018): 1-83, arXiv:1701.03146

[5] L. F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167, arXiv:0906.3219.

[6] F. Aprile, S. Pasquetti, and Y. Zenkevich, Flipping the head of T [SU (N )]: mirror symmetry, spectral duality and monopoles, Journal of High Energy Physics 2019, no. 4 (2019): 1-71, arXiv:1812.08142

[7] H. Awata, and H. Kanno, Refined BPS state counting from Nekrasov’s formula and Macdonald functions, International Journal of Modern Physics A 24, no. 12 (2009): 2253-2306, arXiv:0805.0191.

[8] H. Awata and Y. Yamada, Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra, JHEP 01, 125 (2010), arXiv:0910.4431.

[9] H. Awata, B. Feigin, A. Hoshino, M. Kanai, J. Shiraishi, and S. Yanagida, Notes on Ding-Iohara algebra and AGT conjecture, arXiv:1106.4088.

[10] H. Awata, B. Feigin, and J. Shiraishi, Quantum algebraic approach to refined topological vertex, Journal of High Energy Physics 2012, no. 3 (2012): 1-35, arXiv:1112.6074.

[11] H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, Y. Zenkevich, Anomaly in RTT relation for DIM algebra and network matrix models, Nucl.Phys. B918 (2017) 358, arXiv:1611.07304.

[12] H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Y. Ohkubo, and Y. Zenkevich, Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra, Physical Review D 96, no. 2 (2017): 026021, arXiv:1703.06084.

[13] H. Awata, H. Kanno, A. Mironov, A. Morozov, K. Suetake, and Y. Zenkevich The MacMahon R-matrix Journal of High Energy Physics 2019, no. 4 (2019): 1-34, arXiv:1810.07676.

[14] H. Awata, H. Kanno, A. Mironov and A. Morozov, Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function, JHEP 08, 150 (2020), arXiv:2005.10563.

[15] M. Bullimore, H. Kim, and P. Koroteev, Defects and quantum Seiberg-Witten geometry Journal of High Energy Physics 2015, no. 5 (2015): 1-79, arXiv:1412.6081

[16] I. Burban, and O. Schiffmann, On the Hall algebra of an elliptic curve, I Duke Mathematical Journal 161, no. 7 (2012): 1171-1231, arXiv:0505148.

[17] P. Cheewaphutthisakun, and H. Kanno, MacMahon KZ equation for Ding-Iohara-Miki algebra, Journal of High Energy Physics 2021, no. 4 (2021): 1-47, arXiv:2101.01420

[18] P. Cheewaphutthisakun, and H. Kanno, Quasi-Hopf twist and elliptic Nekrasov factor, Journal of High Energy Physics 2021, no. 12 (2021): 1-45, arXiv:2110.03970.

[19] J. Ding, and K. Iohara, Generalization and deformation of Drinfeld quantum affine algebras, Letters in Mathematical Physics 41.2 (1997): 181-193. arXiv:9608002.

[20] V. G. Drinfeld Quantum groups, Zapiski Nauchnykh Seminarov POMI 155 (1986): 18-49.

[21] V. G. Drinfeld Quasi-Hopf algebras, Leningrad Math. J., 1:1419–1457, 1990.

[22] P. Etingof Difference equations with elliptic coefficients and quantum affine algebras arXiv:9312057

[23] P. Etingof, and A. Varchenko, Traces of intertwiners for quantum groups and difference equations I, Duke Mathematical Journal 104, no. 3 (2000): 391-432. arXiv:9907181

[24] P. Etingof, O. Schiffmann, and A. Varchenko, Traces of intertwiners for quantum groups and difference equations, Letters in Mathematical Physics 62, no. 2 (2002): 143-158. arXiv:0207157

[25] B. Feigin, K. Hashizume, A. Hoshino, J. Shiraishi, and S. Yanagida, A commutative algebra on degenerate CP1 and Macdonald polynomials, Journal of Mathematical Physics 50, no. 9 (2009): 095215, arXiv:0904.2291.

[26] B. Feigin, A. Hoshino, J. Shibahara, J. Shiraishi, and S. Yanagida, Kernel function and quantum algebras, arXiv:1002.2485.

[27] B. Feigin, E. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, Quantum continuous glŒ: Semiinfinite construction of representations, Kyoto Journal of Mathematics 51, no. 2 (2011): 337-364. arXiv:1002.3100.

[28] B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, Quantum toroidal gl1-algebra: Plane partitions, Kyoto Journal of Mathematics 52, no. 3 (2012): 621-659, arXiv:1110.5310.

[29] B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, Quantum toroidal and Bethe ansatz, Journal of Physics A: Mathematical and Theoretical 48, no. 24 (2015): 244001, arXiv:1502.07194

[30] B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, Finite Type Modules and Bethe Ansatz for Quantum Toroidal gl1, Communications in Mathematical Physics 356, no. 1 (2017): 285-327, arXiv:1603.02765

[31] I. B. Frenkel, and N. Y. Reshetikhin, Quantum affine algebras and holonomic difference equations, Communications in mathematical physics 146, no. 1 (1992): 1-60,

[32] M. R. Gaberdiel, and R. Gopakumar, Minimal model holography, Journal of Physics A: Mathematical and Theoretical 46, no. 21 (2013): 214002, arXiv:1207.6697.

[33] M. R. Gaberdiel, R. Gopakumar, W. Li, and C. Peng, Higher spins and Yangian symmetries, Journal of High Energy Physics 2017, no. 4 (2017): 1-29, arXiv:1702.05100.

[34] M. Ghoneim, C. Kozc¸az, K. Kur¸sun, and Y. Zenkevich, 4d higgsed network calculus and elliptic DIM algebra, Nuclear Physics B 978 (2022): 115740, arXiv:2012.15352

[35] U. G¨ortz, and T. Wedhorn, Algebraic Geometry I: Schemes, Vieweg+ Teubner, 2010.

[36] B. Haghighat, A. Iqbal, C. Kozc¸az, G. Lockhart and C. Vafa, M-Strings, Commun. Math. Phys. 334, no.2, 779-842 (2015), arXiv:1305.6322.

[37] B. Haghighat, C. Kozcaz, G. Lockhart and C. Vafa, Orbifolds of M-strings, Phys. Rev. D 89, no.4, 046003 (2014), arXiv:1310.1185.

[38] A. Iqbal, C. Kozcaz and S. T. Yau, Elliptic Virasoro Conformal Blocks, arXiv:1511.00458.

[39] M. Jimbo, 量子群とヤン・バクスター方程式, シュプリンガー現代数学シリーズ(1990).

[40] M. Jimbo, H. Konno, S. Odake, and J. Shiraishi, Quasi-Hopf twistors for elliptic quantum groups, Transformation Groups 4, no. 4 (1999): 303-327, arXiv:9712029.

[41] M. Jimbo, H. Konno, S. Odake, and J. Shiraishi, Elliptic algebra: Drinfeld currents and vertex operators, Communications in mathematical physics 199, no. 3 (1999): 605-647, arXiv:9802002.

[42] H. Konno, Elliptic weight functions and elliptic q-KZ equation, Journal of Integrable Systems 2, no. 1 (2017): xyx011, arXiv:1706.07630.

[43] G. Lockhart and C. Vafa, Superconformal Partition Functions and Non-perturbative Topological Strings, JHEP 10, 051 (2018), arXiv:1210.5909.

[44] R. Lodin, F. Nieri and M. Zabzine, Elliptic modular double and 4d partition functions, J. Phys. A 51, no.4, 045402 (2018), arXiv:1703.04614.

[45] P. Longhi, F. Nieri, and A. Pittelli, Localization of 4d N = 1 theories on D2 × T2, Journal of High Energy Physics 2019, no. 12 (2019): 1-69, arXiv:1906.02051.

[46] I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, Oxford University Press (1995)

[47] J. Maillet, and J. Sanchez De Santos, Drinfel’d twists and algebraic Bethe ansatz, arXiv:9612012.

[48] K. Miki, A (q, g) analog of the W1+Πalgebra, Journal of Mathematical Physics 48, no. 12 (2007): 123520.

[49] A. Mironov, and A. Morozov, On AGT relation in the case of U (3) Nuclear physics B 825, no. 1-2 (2010): 1-37, arXiv:0908.2569.

[50] A. Mironov, A. Morozov and Y. Zenkevich, Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings, JHEP 05, 121 (2016), arXiv:1603.00304.

[51] A. Morozov An analogue of Schur functions for the plane partitions Physics Letters B 785 (2018): 175-183, arXiv:1808.01059.

[52] H. Nakajima, and K. Yoshioka, Instanton counting on blowup. I. 4-dimensional pure gauge theory, Inventiones mathematicae 162, no. 2 (2005): 313-355, arXiv:0306198.

[53] H. Nakajima, and K. Yoshioka, Instanton counting on blowup. II. K-theoretic partition function, Transformation groups 10, no. 3 (2005): 489-519, arXiv:0505553

[54] N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Advances in Theoretical and Mathematical Physics 7 (2003): 831-864, arXiv:0206161

[55] N. A. Nekrasov, and A. Okounkov, Seiberg-Witten theory and random partitions, In The unity of mathematics, pp. 525-596. Birkh¨auser Boston, 2006, arXiv:0306238

[56] A. Negut, The R-matrix of the quantum toroidal algebra arXiv:2005.14182

[57] A. Nedelin, S. Pasquetti, and Y. Zenkevich, T [SU (N )] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences, Journal of High Energy Physics 2019, no. 2 (2019): 1-57, arXiv:1712.08140

[58] M. Nishizawa, An elliptic analogue of the multiple gamma function, J. Phys. A 34 7411 (2001).

[59] F. Nieri, An elliptic Virasoro symmetry in 6d, Lett. Math. Phys. 107, no. 11, 2147 (2017), arXiv:1511.00574.

[60] A. Pittelli, Supersymmetric localization of refined chiral multiplets on topologically twisted H2 ◊ S1, Physics Letters B 801 (2020): 135154, arXiv:1812.11151.

[61] T. Proch´azka, W-symmetry, topological vertex and affine Yangian, Journal of High Energy Physics 2016, no. 10 (2016): 1-73, arXiv:1512.07178

[62] Y. Saito, Elliptic Ding–Iohara algebra and the free field realization of the elliptic Macdonald operator, Publications of the Research Institute for Mathematical Sciences 50, no. 3 (2014): 411-455, arXiv:1301.4912.

[63] O. Schiffmann, Drinfeld realization of the elliptic Hall algebra, Journal of Algebraic Combinatorics 35, no. 2 (2012): 237-262, arXiv:1004.2575

[64] A. Tsymbaliuk, The affine Yangian of gl1, and the infinitesimal Cherednik algebras, Ph.D. Thesis, Department of Mathematics, MIT (2014).

[65] A. Tsymbaliuk, The affine Yangian of gl1 revisited, Advances in Mathematics 304 (2017): 583-645. arXiv:1404.5240

[66] N. Wyllard, A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 0911 (2009) 002, arXiv:0907.2189.

[67] Y. Yoshida, and K. Sugiyama, Localization of 3d N = 2 Supersymmetric Theories on S1 ◊ D2, Progress of Theoretical and Experimental Physics, Volume 2020, Issue 11, November 2020, 113B02, arXiv:1409.6713

[68] Y. Zenkevich, 3d field theory, plane partitions and triple Macdonald polynomials, Journal of High Energy Physics 2019, no. 6 (2019): 1-25. arXiv:1712.10300

[69] R. D. Zhu, An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings, JHEP 08, 050 (2018), arXiv:1712.10255.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る