# zbMATH — the first resource for mathematics

Review of AdS/CFT integrability, chapter VI.1: Superconformal symmetry. (English) Zbl 1268.81126
Summary: Aspects of the $$D = 4$$, $${\mathcal N=4}$$ superconformal symmetry relevant to the AdS/CFT duality and integrability are reviewed. These include the Lie superalgebra $$\mathfrak{psu}(2,2|4)$$, its representations, conformal transformations and correlation functions in $${\mathcal N=4}$$ super Yang-Mills theory as well as an illustration of the $$\text{AdS}_5\times S^5$$ superspace on which the dual string theory is formulated.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 81T60 Supersymmetric field theories in quantum mechanics
Full Text:
##### References:
 [1] Sohnius M.F., West P.C.: Conformal invariance in $${$$\backslash$$mathcal{N} = 4}$$ supersymmetric Yang–Mills theory. Phys. Lett. B 100, 245 (1981) [2] Mandelstam S.: Light cone superspace and the ultraviolet finiteness of the $${$$\backslash$$mathcal{N}= 4}$$ model. Nucl. Phys. B 213, 149 (1983) [3] Brink L., Lindgren O., Nilsson B.E.W.: $${$$\backslash$$mathcal{N}= 4}$$ Yang–Mills theory on the light cone. Nucl. Phys. B 212, 401 (1983) [4] Howe P.S., Stelle K.S., Townsend P.K.: Ultraviolet cancellations in supersymmetry made manifest. Nucl. Phys. B 236, 125 (1984) [5] D’Hoker, E., Freedman, D.Z.: Supersymmetric Gauge Theories and the AdS/CFT Correspondence. hep-th/0201253 [6] Beisert, N., et al.: Review of AdS/CFT Integrability: An Overview. Lett. Math. Phys. Published in this volume. arxiv:1012.3982 [7] Cornwell, J.F.: Group Theory in Physics, vol. III: Supersymmetries and Infinite-Dimensional Algebras. Techniques of Physics 10. Academic Press, London (1989) · Zbl 0686.17001 [8] Frappat L., Sorba P., Sciarrino A.: Dictionary on Lie Algebras and Superalgebras. Academic Press, London (2000) · Zbl 0965.17001 [9] Frappat, L., Sorba, P., Sciarrino, A.: Dictionary on Lie Superalgebras. hep-th/9607161 · Zbl 0965.17001 [10] Cornwell J.F.: Group Theory in Physics: An Introduction. Academic Press, London (1997) · Zbl 0878.20001 [11] Beisert N.: The su(2/3) dynamic spin chain. Nucl. Phys. B 682, 487 (2004) hep-th/0310252 · Zbl 1036.82513 [12] Dobrev V.K., Petkova V.B.: All positive energy unitary irreducible representations of extended conformal supersymmetry. Phys. Lett. B 162, 127 (1985) · Zbl 0585.17003 [13] Sternberg S.: Group Theory and Physics. Cambridge University Press, Cambridge (1994) · Zbl 0816.53002 [14] Mack G., Salam A.: Finite component field representations of the conformal group. Ann. Phys. 53, 174 (1969) [15] Günaydin M., Marcus N.: The spectrum of the S5 compactification of the chiral $${$$\backslash$$mathcal{N} = 2, D = 10}$$ supergravity and the unitary supermultiplets of U(2,2/4). Class. Quantum Gravit. 2, L11 (1985) [16] Minahan, J.A.: Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in $${$$\backslash$$mathcal{N}= 4}$$ SYM. Lett. Math. Phys. Published in this volume. arxiv:1012.3983 · Zbl 1244.81045 [17] Sieg, C.: Review of AdS/CFT Integrability, Chapter I.2: The Spectrum From Perturbative Gauge Theory. Lett. Math. Phys. Published in this volume. arxiv:1012.3984 · Zbl 1244.81046 [18] Rej, A.: Review of AdS/CFT Integrability, Chapter I.3: Long-Range Spin Chains. Lett. Math. Phys. Published in this volume. arxiv:1012.3985 · Zbl 1244.81056 [19] Janik R.A., Surowka P., Wereszczynski A.: On correlation functions of operators dual to classical spinning string states. JHEP 1005, 030 (2010) arxiv:1002.4613 · Zbl 1288.81111 [20] Aharony O., Gubser S.S., Maldacena J.M., Ooguri H., Oz Y.: Large N field theories, string theory and gravity. Phys. Rept. 323, 183 (2000) hep-th/9905111 · Zbl 1368.81009 [21] Magro, M.: Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing. Lett. Math. Phys. Published in this volume. arxiv:1012.3988 · Zbl 1243.81166 [22] Zarembo K.: Strings on semisymmetric superspaces. JHEP 1005, 002 (2010) arxiv:1003.0465 · Zbl 1288.81127
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.