Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory

TL;DR

This paper reviews recent advances in verifying the AdS/CFT duality by analyzing semiclassical string states and their correspondence to long scalar operators in N=4 SYM, using effective action methods.

Contribution

It demonstrates how the sigma model effective action emerges from both the string theory in AdS_5 x S^5 and the spin chain Hamiltonian of N=4 SYM, linking the two descriptions.

Findings

Effective sigma model action matches string and gauge theory descriptions.

Semiclassical string states correspond to long scalar operators.

Unified approach enhances understanding of AdS/CFT duality.

Abstract

We review recent progress in checking AdS/CFT duality in the sector of ''semiclassical'' string states dual to ''long'' scalar operators of N=4 super Yang-Mills theory. In particular, we discuss the effective action approach, in which the same sigma model type action describing coherent states is shown to emerge from the AdS_5 x S^5 string action and from the spin chain Hamiltonian representing the SYM dilatation operator.