Classical and quantum integrability in AdS(2)/CFT(1)
Jeff Murugan, Per Sundin, Linus Wulff
TL;DR
The paper investigates the Type IIA string on $AdS_2\times S^2\times T^6$ with RR flux as the gravity dual to $AdS_2/CFT_1$, focusing on both the coset (massive) and non-coset (massless) worldsheet sectors. It performs a BMN-style expansion of the Green-Schwarz action to quartic order, compares classical near-BMN energies to proposed Bethe equations, and studies quantum corrections to the magnon dispersion, finding vanishing one-loop contributions and a sine-square two-loop structure in the near-flat-space limit, with the massless sector playing a crucial role. The results provide strong evidence for quantum integrability of the full GS string in this background, highlighting the necessity of including massless non-coset modes and their interactions to obtain the correct quantum behavior. This work thus extends integrability checks to a lower-dimensional AdS/CFT context and lays groundwork for incorporating massless excitations into the Bethe ansatz/S-matrix framework, with potential implications for the dual $CFT_1$ dynamics.
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.