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Classical/quantum integrability in AdS/CFT
Open accessAbstract
We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in N = 4 super Yang-Mills and the energy of their dual semiclassical string states in AdS 5 × S 5 . The anomalous dimensions can be computed using a set of Bethe equations, which for “long” operators reduces to a Riemann-Hilbert problem. We develop a unified approach to the long wavelength Bethe equations, the classical ferromagnet and the classical string solutions in the SU (2) sector and present a general solution, governed by complex curves endowed with meromorphic differentials with integer periods. Using this solution we compute the anomalous dimensions of these long operators up to two loops and demonstrate that they agree with string-theory predictions.
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Cites
The large $N$ limit of superconformal field theories and supergravity
Maldacena, J. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a1 · Cited by 14,524
Anti de Sitter space and holography
Witten, E. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a2 · Cited by 13,070
Gauge theory correlators from non-critical string theory
Gubser, S. S., Klebanov, I. R., & Polyakov, A. M. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00377-3 · Cited by 9,307
Gauge Theory Correlators from Non-Critical String Theory
Gubser, S. S., Klebanov, I. R., & Polyakov, A. M. (1998) · arXiv · doi:10.48550/arxiv.hep-th/9802109 · Cited by 9,307
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
Bethe, H. (1931) · Zeitschrift f�r Physik · doi:10.1007/bf01341708 · Cited by 3,768
Brézin, E., Itzykson, C., Parisi, G., & Zuber, J. B. (1978) · Communications in Mathematical Physics · doi:10.1007/bf01614153 · Cited by 1,479
Cited by
Closed strings in Misner space: cosmological production of winding strings
Berkooz, M., Pioline, B., & Rozali, M. (2004) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2004/08/004 · Cited by 54
Metadata
- Authors
- A.Kazakov, V, Marshakov, A., A.Minahan, J., & Zarembo, K.
- Venue
- Journal of High Energy Physics
- Published
- 2004-05-11
- Volume
- 2004
- Issue
- 05
- Pages
- 024-024
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W2009722268
- Cited by
- 567
- References
- 6
- FWCI
- 42.43
- Type
- journal article
- Language
- en
- Open access
- bronze
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- A.Kazakov, V, Marshakov, A., A.Minahan, J., & Zarembo, K. (2004). Classical/quantum integrability in AdS/CFT. Journal of High Energy Physics. https://doi.org/10.1088/1126-6708/2004/05/024
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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