Classical and quantum integrability in AdS(2)/CFT(1)

Abstract

We investigate the type IIA string on AdS(2)xS(2)xT(6) supported by RR-flux which describes the gravitational side of the AdS(2)/CFT(1) correspondence. While the four-dimensional part AdS(2)xS(2) can be realized as a supercoset, the full superstring has both coset and non-coset excitations, the latter giving rise to massless worldsheet modes, a somewhat novel feature in AdS/CFT. The string is nevertheless known to be integrable at the classical level. In this paper we perform several computations checking aspects of both classical and quantum string integrability. At the classical level we compute energies for the near BMN string and successfully match these against Bethe ansatz predictions. Furthermore, integrability dictates a magnon dispersion relation which we compare with the poles of loop corrected propagators, at both the one and two-loop level. At one loop, where only tadpole diagrams contribute, we find that the bosonic and fermionic contributions sum up to zero. Under the assumption of worldsheet supersymmetry, we then compute the two-loop sunset diagram in the near flat space limit. As in AdS(5)xS(5) we find that the result fits nicely into the sine-square structure of the dispersion relation.

18 pages, 2 figures; v2: References added

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Spinning strings at one-loop in AdS_4 x P^3
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• World-sheet scattering in AdS_5 x S^5 at two loops
• Comment on the Scaling Function in AdS4 x CP3
• Quantum Strings and the AdS4/CFT3 Interpolating Function

Cited by in corpus (17)

• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Towards integrability for AdS3/CFT2
• Worldsheet scattering in AdS(3)/CFT(2)
• The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• The S-matrix algebra of the AdS2 X S2 superstring
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Geometry of Massless Scattering in Integrable Superstring
• A study of integrable form factors in massless relativistic $Ad{S}_2$