Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet

TL;DR

This work extends the semiclassical string quantization approach to AdS$_5\times$S$^5$ by incorporating a minimal nonzero S^5 angular momentum $J$, enabling a clearer identification of string states with Konishi multiplet operators. It shows that for the first excited string level with $J=2$, the subleading energy coefficient is $b_1=2$, and that in general $b_1(J)=b_1(0)+\frac{1}{4}J^2$ with $b_1(0)=1$, aligning with Y-system/TBA results. The authors analyze several explicit string solutions—three-spin circular strings and folded strings—to demonstrate the universality of $b_1=2$ across Konishi-related states at $\Delta_0=6$ and $\Delta_0=4$, while also discussing conditions under which $J$-dependent corrections do not affect leading terms. Overall, the results provide a nontrivial cross-check of AdS/CFT and integrability-based predictions, reinforcing the consistency between semiclassical string theory and the gauge-theory Konishi multiplet at strong coupling.

Abstract

Following our earlier work in arXiv:0906.4294 we show how to use semiclassical string quantization approach to compute the leading corrections to the energy of AdS_5 x S^5 string states on the first excited string level that should correspond to operators in the Konishi multiplet of N=4 SYM theory. Compared to examples in our previous paper the string solutions we consider here carry an extra component of S^5 angular momentum J. This facilitates their identification with operators in the Konishi multiplet. We show that for such string states with J=2 the coefficient of the subleading lambda^(-1/4) term in the large string tension expansion of the energy is twice the one found in arXiv:0906.4294. The resulting value matches the one found for the Konishi state in the sl(2) sector from the Y-system/TBA approach, resolving an apparent disagreement claimed earlier.