Analytic Bethe ansatz and Baxter equations for long-range \(\text{psl}(2|2)\) spin chain. (English) Zbl 1225.81133
Summary: We study the largest particle-number-preserving sector of the dilatation operator in maximally supersymmetric gauge theory. After exploring one-loop Bethe ansatz for the underlying spin chain with \(\text{psl}(2|2)\) symmetry for simple root systems related to several Kac-Dynkin diagrams, we use the analytic Bethe ansatz to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space. We derive closed Baxter equations for eigenvalues of nested Baxter operators. We extend these considerations for a non-distinguished root system with FBBF grading to all orders of perturbation theory in ’t Hooft coupling. We construct generating functions for all transfer matrices with auxiliary space determined by Young supertableaux \((1^a)\) and \((s)\) and find determinant formulas for transfer matrices with auxiliary spaces corresponding to skew Young supertableaux. The latter yields fusion relations for transfer matrices with auxiliary space corresponding to representations labelled by square Young supertableaux. We derive asymptotic Baxter equations which determine spectra of anomalous dimensions of composite Wilson operators in noncompact \(\text{psl}(2|2)\) subsector of \(\mathcal N=4\) super-Yang-Mills theory.
This is a continuation of Belitsky et al. [Nucl. Phys., B 768, No. 1–2, 116–134 (2007; Zbl 1117.81100)].
This is a continuation of Belitsky et al. [Nucl. Phys., B 768, No. 1–2, 116–134 (2007; Zbl 1117.81100)].
MSC:
81T60 | Supersymmetric field theories in quantum mechanics |
81T13 | Yang-Mills and other gauge theories in quantum field theory |
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
82B23 | Exactly solvable models; Bethe ansatz |
Keywords:
analytic Bethe ansatz; Lie superalgebra; solvable lattice model; Baxter equations; anomalous dimensionsCitations:
Zbl 1117.81100References:
[1] | Lipatov, L. N., JETP Lett., 59, 596 (1994) |
[2] | Faddeev, L. D.; Korchemsky, G. P., Phys. Lett. B, 342, 311 (1995) |
[3] | Bukhvostov, A. P.; Frolov, G. V.; Kuraev, E. A.; Lipatov, L. N., Nucl. Phys. B, 258, 601 (1985) |
[4] | Braun, V. M.; Derkachov, S. E.; Manashov, A. N., Phys. Rev. Lett., 81, 2020 (1998) |
[5] | Braun, V. M.; Derkachov, S. E.; Korchemsky, G. P.; Manashov, A. N., Nucl. Phys. B, 553, 355 (1999) |
[6] | Belitsky, A. V., Nucl. Phys. B, 574, 407 (2000) |
[7] | Belitsky, A. V.; Gorsky, A. S.; Korchemsky, G. P., Nucl. Phys. B, 667, 3 (2003) · Zbl 1059.81615 |
[8] | Belitsky, A. V.; Derkachov, S. E.; Korchemsky, G. P.; Manashov, A. N., Nucl. Phys. B, 708, 115 (2005) · Zbl 1160.81461 |
[9] | Lipatov, L. N., Evolution equations in QCD, (Boffi, S.; Ciofi Degli Atti, C.; Giannini, M., Perspectives in Hadronic Physics (1998), World Scientific: World Scientific Singapore), 413 |
[10] | Minahan, J. A.; Zarembo, K., J. High Energy Phys., 0303, 013 (2003) |
[11] | Beisert, N.; Kristjansen, C.; Staudacher, M., Nucl. Phys. B, 664, 131 (2003) · Zbl 1051.81044 |
[12] | Beisert, N., Nucl. Phys. B, 676, 3 (2004) · Zbl 1097.81575 |
[13] | Beisert, N.; Staudacher, M., Nucl. Phys. B, 670, 439 (2003) · Zbl 1058.81581 |
[14] | Yang, C. N., Phys. Rev. Lett., 19, 1312 (1967) · Zbl 0152.46301 |
[15] | Beisert, N.; Dippel, V.; Staudacher, M., J. High Energy Phys., 0407, 075 (2004) |
[16] | Staudacher, M., J. High Energy Phys., 0505, 054 (2005) |
[17] | Beisert, N.; Staudacher, M., Nucl. Phys. B, 727, 1 (2005) · Zbl 1126.81328 |
[18] | Baxter, R. J., Exactly Solved Models in Statistical Mechanics (1982), Academic Press: Academic Press London · Zbl 0538.60093 |
[19] | Belitsky, A. V.; Korchemsky, G. P.; Müller, D., Nucl. Phys. B, 768, 116 (2007) · Zbl 1117.81100 |
[20] | Belitsky, A. V., Phys. Lett. B, 643, 354 (2006) · Zbl 1248.81219 |
[21] | Belitsky, A. V., Phys. Lett. B, 650, 72 (2007) |
[22] | Reshetikhin, N. Yu., Lett. Math. Phys., 14, 235 (1987) · Zbl 0636.17006 |
[23] | Beisert, N., Phys. Rep., 407, 1 (2004) |
[24] | Beisert, N.; Kazakov, V. A.; Sakai, K.; Zarembo, K., J. High Energy Phys., 0507, 030 (2005) |
[25] | Zwiebel, B. I., J. High Energy Phys., 0602, 055 (2006) |
[26] | A.V. Belitsky, G.P. Korchemsky, 2005, unpublished; A.V. Belitsky, G.P. Korchemsky, 2005, unpublished |
[27] | Brink, L.; Lindgren, O.; Nilsson, B. E., Phys. Lett. B, 123, 323 (1983) |
[28] | Mandelstam, S., Phys. Lett. B, 121, 30 (1983) |
[29] | Belitsky, A. V.; Derkachov, S. E.; Korchemsky, G. P.; Manashov, A. N., Nucl. Phys. B, 722, 191 (2005) · Zbl 1128.81322 |
[30] | Kulish, P. P., J. Sov. Math., 35, 2648 (1986) |
[31] | Reshetikhin, N. Yu., Lett. Math. Phys., 14, 235 (1987) · Zbl 0636.17006 |
[32] | Kulish, P. P.; Sklyanin, E. K., J. Sov. Math., 19, 1596 (1982) · Zbl 0497.35072 |
[33] | Eßler, F. H.L.; Korepin, V. E.; Schoutens, K., Int. J. Mod. Phys. B, 8, 3205 (1994) |
[34] | Eßler, F. H.L.; Korepin, V. E., Int. J. Mod. Phys. B, 8, 3243 (1994) |
[35] | Schoutens, K., Nucl. Phys. B, 413, 675 (1994) · Zbl 1007.82501 |
[36] | Kulish, P. P.; Sklyanin, E. K., Lect. Notes Phys., 151, 61 (1982) |
[37] | Tsuboi, Z., J. Phys. A, 31, 5485 (1998) · Zbl 0954.81023 |
[38] | Bazhanov, V. V.; Reshetikhin, N. Yu., J. Phys. A, 23, 1477 (1990) · Zbl 0712.17024 |
[39] | Kuniba, A.; Suzuki, J., Commun. Math. Phys., 173, 225 (1995) · Zbl 0834.58045 |
[40] | Balantekin, A. B.; Bars, I., J. Math. Phys., 22, 1149 (1981) · Zbl 0469.22017 |
[41] | Kac, V. G., Adv. Math., 26, 8 (1977) · Zbl 0366.17012 |
[42] | Grozman, P.; Leites, D., Czech. J. Phys., 51, 1 (2001) · Zbl 0979.17002 |
[43] | Frappat, L.; Sorba, P.; Sciarrino, A., Dictionary on Lie Superalgebras (2000), Academic Press: Academic Press London · Zbl 0965.17001 |
[44] | Bares, P.; Carmelo, J. M.P.; Ferrer, J.; Horsch, P., Phys. Rev. B, 46, 14624 (1992) |
[45] | Eßler, F. H.L.; Korepin, V. E., Phys. Rev. B, 46, 9147 (1992) |
[46] | Foerster, A.; Karowski, M., Nucl. Phys. B, 396, 611 (1993) |
[47] | Göhmann, F.; Seel, A., J. Phys. A, 37, 2843 (2004) · Zbl 1038.82004 |
[48] | Cherednik, I. V., Duke Math. J., 54, 563 (1987) · Zbl 0645.17006 |
[49] | Fulton, W., Young Tableaux (1997), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0878.14034 |
[50] | Krichever, I.; Lipan, O.; Wiegmann, P.; Zabrodin, A., Commun. Math. Phys., 188, 267 (1997) · Zbl 0896.58035 |
[51] | Kirillov, A. N.; Reshetikhin, N. Yu., J. Phys. A, 20, 1565 (1987) |
[52] | Kuniba, A.; Ohta, Y.; Suzuki, J., J. Phys. A, 28, 6211 (1995) · Zbl 0871.17015 |
[53] | Klümper, A.; Pearce, P., Physica A, 183, 304 (1992) · Zbl 1201.82009 |
[54] | Kuniba, A.; Nakanishi, T.; Suzuki, J., Int. J. Mod. Phys. A, 9, 5215 (1994) |
[55] | Kazakov, V.; Sorin, A.; Zabrodin, A., Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics · Zbl 1150.82009 |
[56] | Beisert, N.; Eden, B.; Staudacher, M., J. Stat. Mech., 0701, P021 (2007) |
[57] | Dorey, N.; Hofman, D. M.; Maldacena, J., On the singularities of the magnon S-matrix · Zbl 1222.81267 |
[58] | Beisert, N., J. Stat. Mech., 0701, P017 (2007) |
[59] | Lipan, O.; Wiegmann, P. B.; Zabrodin, A., Mod. Phys. Lett. A, 12, 1369 (1997) · Zbl 1022.81580 |
[60] | Sklyanin, E. K., Progr. Theor. Phys. Suppl., 118, 35 (1995) · Zbl 0464.35071 |
[61] | Janik, R. A., Phys. Rev. D, 73, 086006 (2006) |
[62] | Beisert, N., The \(su(2 | 2)\) dynamic \(S\)-matrix · Zbl 1275.81084 |
[63] | Belitsky, A. V.; Derkachov, S. E.; Korchemsky, G. P.; Manashov, A. N., Phys. Rev. D, 70, 045021 (2004) |
[64] | Gates, S. J.; Grisaru, M. T.; Rocek, M.; Siegel, W., Front. Phys., 58, 1 (1983) |
[65] | Gunaydin, M.; Saclioglu, C., Commun. Math. Phys., 87, 159 (1982) · Zbl 0498.22019 |
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