Orthosymplectic superoscillator Lax matrices. (English) Zbl 07837886
Summary: We construct Lax matrices of superoscillator type that are solutions of the RTT-relation for the rational orthosymplectic \(R\)-matrix, generalizing orthogonal and symplectic oscillator type Lax matrices previously constructed by the authors in Frassek (Nuclear Phys B, 2020), Frassek and Tsymbaliuk (Commun Math Phys 392 (2):545-619, 2022), Frassek et al. (Commun Math Phys 400 (1):1-82, 2023). We further establish factorisation formulas among the presented solutions.
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
Keywords:
Yang-Baxter equation; Lax matrices; shifted Yangians; orthosymplectic Yangians; \(Q\)-operatorsReferences:
| [1] | Arnaudon, D.; Avan, J.; Crampé, N.; Frappat, L.; Ragoucy, E., \(R\)-matrix presentation for super-Yangians \(Y(osp(m|2n))\), J. Math. Phys., 44, 1, 302-308, 2003 · Zbl 1061.17014 · doi:10.1063/1.1525406 |
| [2] | Bombardelli, D.; Cavaglià, A.; Fioravanti, D.; Gromov, N.; Tateo, R., The full quantum spectral curve for \(AdS_4/CFT_3\), J. High Energy Phys., 140, 9, 72pp, 2017 · Zbl 1382.81171 |
| [3] | Braverman, A., Finkelberg, M., Nakajima, H.: Coulomb branches of \(3d\cal{N}=4\) quiver gauge theories and slices in the affine Grassmannian (with appendices by A. Braverman, M. Finkelberg, J. Kamnitzer, R. Kodera, H. Nakajima, B. Webster, A. Weekes), Adv. Theor. Math. Phys. 23(1), 75-166 (2019) · Zbl 1479.81044 |
| [4] | Bazhanov, V.; Hibberd, A.; Khoroshkin, S., Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory, Nuclear Phys. B, 622, 3, 475-547, 2002 · Zbl 0983.81088 · doi:10.1016/S0550-3213(01)00595-8 |
| [5] | Brundan, J.; Kleshchev, A., Parabolic presentations of the Yangian \(Y({\mathfrak{gl} }_n)\), Commun. Math. Phys., 254, 1, 191-220, 2005 · Zbl 1128.17012 · doi:10.1007/s00220-004-1249-6 |
| [6] | Bazhanov, V.; Lukyanov, S.; Zamolodchikov, A., Integrable structure of conformal field theory II. Q-operator and DDV equation, Commun. Math. Phys., 190, 2, 247-278, 1997 · Zbl 0908.35114 · doi:10.1007/s002200050240 |
| [7] | Bazhanov, V.; Tsuboi, Z., Baxter’s \(Q\)-operators for supersymmetric spin chains, Nuclear Phys. B, 805, 3, 451-516, 2008 · Zbl 1190.82007 · doi:10.1016/j.nuclphysb.2008.06.025 |
| [8] | Costello, K., Gaiotto, D., Yagi, J.: \(Q\)-operators are \(^{\prime }{{\rm t}}\) Hooft lines, preprint, arXiv:2103.01835 (2021) |
| [9] | Frassek, R.: Oscillator realisations associated to the \(D\)-type Yangian: towards the operatorial \(Q\)-system of orthogonal spin chains. Nuclear Phys. B 956, Paper No. 115063, 22pp (2020) · Zbl 1479.82015 |
| [10] | Frassek, R.: Lax matrices for Baxter Q-operators, Seminar at the University of Bologna (Sept. 4, 2023), 10th Bologna Workshop on Conformal Field Theory and Integrable Models (Sept. 4-7, 2023) |
| [11] | Fuksa, J.; Isaev, A.; Karakhanyan, D.; Kirschner, R., Yangians and Yang-Baxter \(R\)-operators for ortho-symplectic superalgebras, Nuclear Phys. B, 917, 44-85, 2017 · Zbl 1371.17003 · doi:10.1016/j.nuclphysb.2017.01.029 |
| [12] | Frassek, R.; Karpov, I.; Tsymbaliuk, A., Transfer matrices of rational spin chains via novel BGG-type resolutions, Commun. Math. Phys., 400, 1, 1-82, 2023 · Zbl 1530.17008 · doi:10.1007/s00220-022-04620-6 |
| [13] | Frassek, R.; Lukowski, T.; Meneghelli, C.; Staudacher, M., Oscillator construction of \(\mathfrak{su} (n|m)\) Q-operators, Nuclear Phys. B, 850, 1, 175-198, 2011 · Zbl 1215.81047 · doi:10.1016/j.nuclphysb.2011.04.008 |
| [14] | Frassek, R., Pestun, V.: A family of \({{\rm G}}L_r\) multiplicative Higgs bundles on rational base, SIGMA 15, Paper No. 031, 42pp (2019) · Zbl 1464.16029 |
| [15] | Frassek, R., Pestun, V., Tsymbaliuk, A.: Lax matrices from antidominantly shifted Yangians and quantum affine algebras: a-type. Adv. Math. 401, Paper No. 108283, 73pp (2022) · Zbl 1514.17013 |
| [16] | Frassek, R.; Tsymbaliuk, A., Rational Lax matrices from antidominantly shifted extended Yangians: BCD types, Commun. Math. Phys., 392, 2, 545-619, 2022 · Zbl 1514.17014 · doi:10.1007/s00220-022-04345-6 |
| [17] | Frassek, R., Tsymbaliuk, A.: Orthosymplectic Yangians, preprint, arXiv:2311.18818 (2023) |
| [18] | Gow, L.: Yangians of Lie superalgebras, Ph.D. Thesis (2007), University of Sydney |
| [19] | Galleas, W.; Martins, M., \(R\)-matrices and spectrum of vertex models based on superalgebras, Nuclear Phys. B, 699, 3, 455-486, 2004 · Zbl 1123.82324 · doi:10.1016/j.nuclphysb.2004.08.002 |
| [20] | Hernandez, D., Zhang, H.: Shifted Yangians and polynomial R-matrices, preprint, arXiv:2103.10993 (2021) |
| [21] | Isaev, A., Karakhanyan, D., Kirschner, R.: Yang-Baxter \(R\)-operators for osp superalgebras, Nuclear Phys. B 965, Paper No. 115355, 28pp (2021) · Zbl 1489.81035 |
| [22] | Kulish, P., Integrable graded magnets, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 145, 140-163, 1985 |
| [23] | Kazakov, V.; Leurent, S.; Tsuboi, Z., Baxter’s \(Q\)-operators and operatorial Bäcklund flow for quantum (super)-spin chains, Commun. Math. Phys., 311, 3, 787-814, 2012 · Zbl 1247.82023 · doi:10.1007/s00220-012-1428-9 |
| [24] | Kuniba, A., Nakanishi, T., Suzuki, J.: \(T\)-systems and \(Y\)-systems in integrable systems. J. Phys. A 44(10), Paper No. 103001, 146pp (2011) · Zbl 1222.82041 |
| [25] | Kulish, P.; Sklyanin, E., Solutions of the Yang-Baxter equation, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 95, 129-160, 1980 |
| [26] | Kazakov, V.; Sorin, A.; Zabrodin, A., Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics, Nuclear Phys. B, 790, 3, 345-413, 2008 · Zbl 1150.82009 · doi:10.1016/j.nuclphysb.2007.06.025 |
| [27] | Molev, A.: A Drinfeld-type presentation of the orthosymplectic Yangians, Alg. Represent. Theory (2023), 26pp |
| [28] | Molev, A., Ragoucy, E.: Gaussian generators for the Yangian associated with the Lie superalgebra \({\mathfrak{osp}}(1|2m)\), preprint, arXiv:2302.00977 (2023) |
| [29] | Marboe, C., Volin, D.: Fast analytic solver of rational Bethe equations. J. Phys. A 50(20), Paper No. 204002 (2017) · Zbl 1367.81081 |
| [30] | Nazarov, M., Quantum Berezinian and the classical Capelli identity, Lett. Math. Phys., 21, 2, 123-131, 1991 · Zbl 0722.17004 · doi:10.1007/BF00401646 |
| [31] | Tsuboi, Z., Analytic Bethe ansatz and functional equations for Lie superalgebra, J. Phys. A, 30, 22, 7975-7991, 1997 · Zbl 0940.81025 · doi:10.1088/0305-4470/30/22/031 |
| [32] | Tsuboi, Z., Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra \({\mathfrak{sl} }(r+1|s+1)\), Phys. A, 252, 3-4, 565-585, 1998 · doi:10.1016/S0378-4371(97)00625-0 |
| [33] | Tsuboi, Z., Solutions of the \(T\)-system and Baxter equations for supersymmetric spin chains, Nuclear Phys. B, 826, 3, 399-455, 2010 · Zbl 1203.82029 · doi:10.1016/j.nuclphysb.2009.08.009 |
| [34] | Tsuboi, Z., Asymptotic representations and \(q\)-oscillator solutions of the graded Yang-Baxter equation related to Baxter \(Q\)-operators, Nuclear Phys. B, 886, 1-30, 2014 · Zbl 1325.81103 · doi:10.1016/j.nuclphysb.2014.06.017 |
| [35] | Tsuboi, Z.: A note on \(q\)-oscillator realizations of \(U_q(gl(M|N))\) for Baxter \(Q\)-operators. Nuclear Phys. B 947 (2019), Paper No. 114747, 33pp · Zbl 1435.81102 |
| [36] | Tsuboi, Z.: Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains, preprint, arXiv:2309.16660 (2023) |
| [37] | Zamolodchikov, A.; Zamolodchikov, A., Factorized \(S\)-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models, Ann. Phys., 120, 2, 253-291, 1979 · doi:10.1016/0003-4916(79)90391-9 |
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