Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator

TL;DR

This paper predicts the strong-coupling expansion of the Konishi operator's anomalous dimension in N=4 SYM using string theory in AdS_5 x S^5, providing explicit coefficients and their mathematical nature.

Contribution

It derives the structure of the strong-coupling expansion of the Konishi operator's anomalous dimension and calculates leading coefficients using semiclassical string states and 1-loop results.

Findings

Explicit form of the strong-coupling expansion with coefficients b_0 and b_1

b_0 is related to the canonical dimension of the gauge operator

b_1 is determined to be 1

Abstract

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=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 Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_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.