Abstract
The aim of the chapter is to introduce in a pedagogical manner the concept of Thermodynamic Bethe Ansatz designed to calculate the energy levels of finite volume integrable systems and to review how it is applied in the planar AdS/CFT setting.
Similar content being viewed by others
References
Zamolodchikov A.B.: Thermodynamic Bethe Ansatz in relativistic models, scaling three state Potts and Lee–Yang models. Nucl. Phys. B 342, 695 (1990). doi:10.1016/0550-3213(90)90333-9
Yang C.-N., Yang C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta–function interaction. J. Math. Phys. 10, 1115 (1969)
Dorey, P., Tateo, R.: Excited states by analytic continuation of TBA equations. Nucl. Phys. B482, 639 (1996). doi:10.1016/S0550-3213(96)00516-0 (hep-th/9607167)
Dorey, P., Tateo, R.: Excited states in some simple perturbed conformal field theories. Nucl. Phys. B515, 575 (1998). doi:10.1016/S0550-3213(97)00838-9 (hep-th/9706140)
Bajnok, Z., Hegedus, A., Janik, R.A., Lukowski, T.: Five loop Konishi from AdS/CFT. (arxiv:0906.4062)
Arutyunov, G., Frolov, S.: The Dressing Factor and Crossing Equations. (arxiv:0904.4575)
Arutyunov G., Frolov S.: Simplified TBA equations of the AdS5 × S5 mirror model. (arxiv:0907.2647)
Cavaglia, A., Fioravanti, D., Tateo, R.: Extended Y-system for the AdS5/CFT4 correspondence. (arxiv:1005.3016)
Ambjorn, J., Janik, R.A., Kristjansen, C.: Wrap** interactions and a new source of corrections to the spin-chain/string duality. Nucl. Phys. B736, 288 (2006). doi:10.1016/j.nuclphysb.2005.12.007 (hep-th/0510171)
Ahn, C., Nepomechie, R.: Review of AdS/CFT integrability, chapter III.2: exact world-sheet S-matrix. Lett. Math. Phys. Published in this volume. (arxiv:1012.3991)
Vieira, P., Volin, D.: Review of AdS/CFT integrability, chapter III.3: the dressing factor. Lett. Math. Phys. Published in this volume. (arxiv:1012.3992)
Beisert N., Staudacher, M.: Long-range PSU(2,2/4) Bethe ansaetze for gauge theory and strings. Nucl. Phys. B727, 1 (2005). doi:10.1016/j.nuclphysb.2005.06.038 (hep-th/0504190)
Rej, A.: Review of AdS/CFT integrability, chapter I.3: long-range spin chains. Lett. Math. Phys. Published in this volume. (arxiv:1012.3985)
Staudacher, M.: Review of AdS/CFT integrability, chapter III.1: Bethe Ansätze and the R-matrix formalism. Lett. Math. Phys. Published in this volume. (arxiv:1012.3990)
Arutyunov, G., Frolov, S.: On string S-matrix, bound states and TBA. JHEP 0712, 024 (2007). doi:10.1088/1126-6708/2007/12/024 (arxiv:0710.1568)
Essler, F.H.L., Frahm, H., Goehmann, F., Kluemper, A., Korepin, V.E.: The One-Dimensional Hubbard Model. Cambridge University Press, London
Arutyunov, G., Frolov, S.: String hypothesis for the AdS5 × S5 mirror. JHEP 0903, 152 (2009). doi:10.1088/1126-6708/2009/03/152 (arxiv:0901.1417)
Bombardelli, D., Fioravanti, D., Tateo, R.: Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal. (arxiv:0902.3930)
Arutyunov, G., Frolov, S.: Thermodynamic Bethe Ansatz for the AdS5 × S5 mirror model. JHEP 0905, 068 (2009). doi:10.1088/1126-6708/2009/05/068 (arxiv:0903.0141)
Gromov, N., Kazakov, V., Kozak, A., Vieira, P.: Integrability for the Full Spectrum of Planar AdS/CFT II. (arxiv:0902.4458)
Gromov, N., Kazakov, V., Vieira, P.: Integrability for the Full Spectrum of Planar AdS/CFT. (arxiv:0901.3753)
Volin, D.: Minimal solution of the AdS/CFT crossing equation. (arxiv:0904.4929)
Frolov, S., Suzuki, R.: Temperature quantization from the TBA equations. Phys. Lett. B679, 60 (2009). doi:10.1016/j.physletb.2009.06.069 (arxiv:0906.0499)
Kazakov, V., Gromov, N.: Review of AdS/CFT integrability, chapter III.7: Hirota dynamics for quantum integrability. Lett. Math. Phys. Published in this volume. (arxiv:1012.3996)
Gromov, N., Kazakov, V., Tsuboi, Z.: PSU(2,2|4) character of quasiclassical AdS/CFT. JHEP 1007, 097 (2010). doi:10.1007/JHEP07(2010)097 (arxiv:1002.3981)
Volin, D.: String hypothesis for gl(n|m) spin chains: a particle/hole democracy. (arxiv:1012.3454)
Gromov, N., Kazakov, V., Vieira, P.: Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics. (arxiv:0812.5091)
Arutyunov, G., Frolov, S., Suzuki, R.: Exploring the mirror TBA. (arxiv:0911.2224)
Gromov, N., Kazakov, V., Vieira, P.: Exact AdS/CFT spectrum: Konishi dimension at any coupling. (arxiv:0906.4240)
Frolov, S.: Konishi operator at intermediate coupling. (arxiv:1006.5032)
Gromov, N., Kazakov, V., Leurent, S., Tsuboi, Z.: Wronskian Solution for AdS/CFT Y-system. (arxiv:1010.2720)
Janik, R.: Review of AdS/CFT integrability, chapter III.5: Lüscher corrections. Lett. Math. Phys. Published in this volume. (arxiv:1012.3994)
Arutyunov, G., Frolov, S., Suzuki, R.: Five-loop Konishi from the mirror TBA. (arxiv:1002.1711)
Balog, J., Hegedus, A.: 5-loop Konishi from linearized TBA and the XXX magnet. (arxiv:1002.4142)
Lukowski, T., Rej, A., Velizhanin, V.N.: Five-Loop Anomalous Dimension of Twist-Two Operators. (arxiv:0912.1624)
Balog, J., Hegedus, A.: The Bajnok-Janik formula and wrap** corrections. (arxiv:1003.4303)
Gromov, N.: Y-system and Quasi-Classical Strings. (arxiv:0910.3608)
Hegedus, A.: Discrete Hirota dynamics for AdS/CFT. (arxiv:0906.2546)
Klose, T.: Review of AdS/CFT integrability, chapter IV.3: \({\mathcal{N}=6}\) Chern–Simons and strings on AdS4 × CP 3. Lett. Math. Phys. Published in this volume. (arxiv:1012.3999)
Bombardelli, D., Fioravanti, D., Tateo, R.: TBA and Y-system for planar AdS 4/CFT 3. Nucl. Phys. B834, 543 (2010). doi:10.1016/j.nuclphysb.2010.04.005 (arxiv:0912.4715)
Gromov, N., Levkovich-Maslyuk, F.: Y-system, TBA and quasi-classical Strings in AdS4 x CP3. JHEP 1006, 088 (2010). doi:10.1007/JHEP06(2010)088 (arxiv:0912.4911)
Arutyunov, G., Frolov, S.: Uniform light-cone gauge for strings in AdS5 × S5: solving su(1/1) sector. JHEP 0601, 055 (2006). doi:10.1088/1126-6708/2006/01/055(hep-th/0510208)
Roiban, R., Tseytlin, A.A.: Quantum strings in AdS5 × S5: strong-coupling corrections to dimension of Konishi operator. (arxiv:0906.4294)
Freyhult, L.: Review of AdS/CFT integrability, chapter III.4: twist states and the cusp anomalous dimension. Lett. Math. Phys. Published in this volume. (arxiv:1012.3993)
Kazakov, V., Leurent, S.: Finite size spectrum of SU(N) principal chiral field from discrete hirota dynamics. (arxiv:1007.1770)
Gromov, N., Serban, D., Shenderovich, I., Volin, D.: Quantum folded string and integrability: from finite size effects to Konishi dimension. (ar**v:1102.1040)
Roiban, R., Tseytlin, A.A.: Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet. (ar**v:1102.1209)
Vallilo, B.C., Mazzucato, L.: The Konishi multiplet at strong coupling. (ar**v: 1102.1219)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bajnok, Z. Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz. Lett Math Phys 99, 299–320 (2012). https://doi.org/10.1007/s11005-011-0512-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-011-0512-y