Higher impurity AdS/CFT correspondence in the near-BMN limit

Abstract

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N = 4 super Yang-Mills (SYM) operators to two loops in the 't Hooft coupling λ. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O(1/J) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in λ and, once again, the string and gauge theory predictions fail to agree at third order.

A universality test of the quantum string Bethe ansatz

“…With c r,s = δ s,r+1 the above string S-matrix gives rise to the correct continuum Bethe equations describing the motion of classical strings on AdS 5 × S 5 [13][14][15][16][17][18] and describes correctly strings in the BMN-limit [19] and the near BMN-limit [20]. In particular, this string S-matrix accounts for the observed three-loop discrepancy between gauge theory and string theory [21][22][23]. In all of these instances the string energies are analytic in λ.…”

Classical integrability and quantum aspects of the AdS 3 × S 3 × S 3 × S 1 superstring

“…As a final remark let us note that in the 'decompactifying' T 4 limit, both the AC and WS regulators give no one-loop corrections. This is expected since both for the AdS 5 × S 5 and AdS 2 × S 2 × T 6 string the one-loop corrections are identically zero [64,65].…”

Near BMN dynamics of the AdS 3 × S 3 × S 3 × S 1 superstring

“…The way to calculate these for closed strings in various AdS / CFT backgrounds is, by now, a rather well-established procedure [60][61][62][63]45,64,43,65]. The starting point is the free quadratic BMN Lagrangian, which allows for an exact solution in terms of string oscillators.…”