More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

Abstract

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.

28 pages; v2: References added

References in corpus (5)

• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• The AdS4/CFT3 algebraic curve
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

Cited by in corpus (29)

• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Worldsheet scattering in AdS(3)/CFT(2)
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Superisometries and integrability of superstrings
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• On integrability of strings on symmetric spaces
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• The low energy limit of the AdS(3) x S(3) x M(4) spinning string
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• The S-matrix algebra of the AdS2 X S2 superstring
• Classical and quantum integrability in AdS(2)/CFT(1)
• Classifying integrable symmetric space strings via factorized scattering
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Non-abelian fermionic T-duality in supergravity
• Orbit method quantization of the AdS${}_2$ superparticle
• All symmetric AdS(n>2) solutions of type II supergravity
• Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Coset construction of AdS particle dynamics
• Geometry of Massless Scattering in Integrable Superstring
• Lagrangian mechanics of massless superparticle on AdS_4 x CP^3 superbackground
• A note about fermionic equations of AdS_4 x CP^3 superstring
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• On integrability of D0-brane equations on AdS_4 x CP^3 superbackground