Superisometries and integrability of superstrings

Abstract

For type II supergravity backgrounds with superisometries the corresponding transformations and conserved currents for the superstring are constructed up to fourth order in $\Theta$. It is then shown how, for certain backgrounds related to near horizon geometries of intersecting branes, the components of the superisometry current can be used to construct a Lax connection demonstrating the classical integrability of the string in these backgrounds. This includes examples of $Ad{S}_2$ and $Ad{S}_3$ backgrounds with a $D(2,1;\alpha )$ isometry group which have not previously been studied from an integrability point of view. The construction of the Lax connection is carried out up to second order in $\Theta$.

31 pages; v2: References added; v3: Published version

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• (Non)-Integrability of Geodesics in D-brane Backgrounds
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• Scattering in AdS(2)/CFT(1) and the BES Phase

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• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
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• On integrability of strings on symmetric spaces
• Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
• The complete one-loop BMN S-matrix in AdS(3) x S(3) x T(4)
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
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• On the spectrum of AdS3 x S3 x T4 strings with Ramond-Ramond flux
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• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• Rigid 4D N=2 supersymmetric backgrounds and actions
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• The S-matrix algebra of the AdS2 X S2 superstring
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• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Orbit method quantization of the AdS${}_2$ superparticle
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• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Fermionic T-Duality of $Ad{S}_n\times S^n(\times S^n)\times T^m$ using IIA Supergravity
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• N spike D-strings in AdS Space with mixed flux
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