Ryo SUZUKI
Theoretical Physics Group
Shing-Tung Yau Center of Southeast University
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Advanced Course on Integrability in the AdS/CFT Correspondence

Course Description

The AdS/CFT correspondence is one of the most profound discoveries in theoretical physics, establishing a duality between certain gauge theories and string theory in anti–de Sitter space. In the planar limit, both sides of this duality become exactly solvable due to an underlying integrable structure.

This lecture series offers a systematic introduction to the role of integrability in AdS/CFT. Aimed at graduate students and young postdocs, the course covers the essential background: four-dimensional conformal field theory, string theory in AdS space, and Maldacena’s duality. We then explore how the one-loop dilatation operator of 𝒩=4 super Yang–Mills theory maps to the Heisenberg spin chain, and how classical string theory on AdS5×S5 gives rise to integrable sigma models. The final part introduces the asymptotic Bethe ansatz, the exact magnon S-matrix, and the dressing phase, leading to the modern understanding of the spectral problem.

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Location: 15th Floor, Yifu Architecture Building, Campus, Southeast University, Nanjing

Time: Saturdays, 16:30–18:00 (Start Date: 28 March 2026)

Prerequisites: Background in quantum field theory, basic general relativity, and representation theory of Lie groups (especially SU(N)). No prior knowledge of string theory or integrable systems is assumed.

Additional Information: These lectures carry no academic credit. Lectures will be given in English. Please write an email to <ryosuzuki@seu.edu.cn> if you are interested in attending or have any questions.

Topics Covered

References (to be added)

  1. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, 1993.
  2. P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory, Springer, 1997.
  3. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, “Large N Field Theories, String Theory and Gravity,” Phys. Rept. 323 (2000) 183 [hep-th/9905111].
  4. E. D’Hoker and D. Z. Freedman, “Supersymmetric Gauge Theories and the AdS/CFT Correspondence,” TASI 2001 Lectures [hep-th/0201253].
  5. L. D. Faddeev, “How algebraic Bethe ansatz works for integrable model,” Les-Houches lectures [hep-th/9605187].
  6. J. A. Minahan and K. Zarembo, “The Bethe ansatz for 𝒩=4 SYM,” JHEP 0303 (2003) 013 [hep-th/0212208].
  7. O. Babelon, D. Bernard, and M. Talon, Introduction to Classical Integrable Systems, Cambridge University Press, 2003.
  8. N. Beisert, “The su(2|2) dynamic S-matrix,” Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th//0209067].
  9. K. Skenderis, Lecture notes on holographic renormalization [arXiv:0908.0333].
  10. D. Tong, Lectures on String Theory [arXiv:0908.0333].
  11. G. Arutyunov and S. Frolov, “Foundations of the AdS5×S5 Superstring. Part I,” J. Phys. A 42 (2009) 254003 [arXiv:0901.4937].
  12. N. Beisert et al., “Review of AdS/CFT Integrability: An Overview,” Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982].

Schedule

[1] Mar 28, Sat

A crash course on the AdS/CFT correspondence and string theory, [Note]

[2] Apr 4, Sat

AdS/CFT before integrability (1); Superconformal symmetry and 𝒩=4 SYM, [Note]

[3] Apr 11, Sat

AdS/CFT before integrability (2); GKP-Witten relations, Particle motion in AdS5×S5, [Note]

[4] Apr 18, Sat

Quantum integrability (1); one-loop problem in 𝒩=4 SYM, [Note]

[5] Apr 25, Sat

Quantum integrability (2); solving spin-1/2 XXX model, singular solutions, Sepatation-of-Variable basis, [Note]

May 2, Sat (holiday)

[6] May 9, Sat

Classical integrability (1); Lax pair

Plan