Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theory

TL;DR

This work studies macroscopic spinning strings in $AdS_5 \times T^{1,1}$ to test the AdS/CFT correspondence in an ${\mathcal N}=1$ setting, mapping string energies $E$ and global charges $(J_A,J_B,J_R)$ to operator dimensions in the dual SCFT with symmetry $SU(2)\times SU(2)\times U(1)$. It derives explicit elliptic-integral expressions for energy–charge relations in single- and multi-spin string solutions, and identifies dual operators in holomorphic ${\rm SU(2)}$ subsectors, concluding that the planar one-loop dilatation operator is isomorphic to the Heisenberg spin chain in that subsector. The results show that states saturating the unitarity bound $E \ge 3|J_R|$ correspond to holomorphic operators, while nonholomorphic configurations remain ambiguous due to operator mixing. The paper discusses integrability prospects for the string sigma model on $AdS_5\times T^{1,1}$ and draws connections to the Neumann model, proposing directions for perturbative gauge-theory checks and extensions beyond the $SU(2)$ subsector.

Abstract

We study rotating strings with multiple spins in the background of $AdS_5\times T^{1,1}$, which is dual to a $\mathcal{N}=1$ superconformal field theory with global symmetry $SU(2)\times SU(2)\times U(1)$ via the AdS/CFT correspondence. We analyse the limiting behaviour of macroscopic strings and discuss the identification of the dual operators and how their anomalous dimensions should behave as the global charges vary. A class of string solutions we find are dual to operators in SU(2) subsector, and our result implies that the one-loop planar dilatation operator restricted to the SU(2) subsector should be equivalent to the hamiltonian of the integrable Heisenberg spin chain.