Quantum strings in AdS ₅ × S ⁵: Strong-coupling corrections to dimension of Konishi operator

We consider leading strong coupling corrections to the energy of the lightest massive string modes in \adss, which should be dual to members of the Konishi operator multiplet in = 4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Δ = 2λ ^1/4+b ₀+b ₁λ ^-1/4+b ₃λ ^-3/4+..., where b ₀ and b ₁ are rational while b ₃ is transcendental (containing ζ(3)). Explicitly, we argue that b ₀ = Δ ₀-4 (where Δ ₀ is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b ₁ = 1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.