Semiclassical circular strings in AdS_5 and "long" gauge field strength operators

TL;DR

This paper explores the duality between semiclassical rotating strings in AdS_5 and long gauge operators, showing linear energy scaling and connecting string solutions to spin chain states.

Contribution

It demonstrates the linear energy dependence of classical and quantum string states and links these to specific spin chain states in gauge theory.

Findings

Classical energy and 1-loop corrections scale linearly with spin S.

Rigid rotating strings correspond to maximal-spin ferromagnetic states.

Pulsating strings relate to lower-spin anti-ferromagnetic states.

Abstract

We consider circular strings rotating with equal spins S_1=S_2=S in two orthogonal planes in AdS_5 and suggest that they may be dual to "long" gauge theory operators built out of self-dual components of gauge field strength. As was found in hep-th/0404187, the one-loop anomalous dimensions of the such gauge-theory operators are described by an anti-ferromagnetic XXX_1 spin chain and scale linearly with length L>>1. We find that in the case of rigid rotating string both the classical energy E_0 and the 1-loop string correction E_1 depend linearly on the spin S (within the stability region of the solution). This supports the relation between the rigid rotating string and the gauge-theory operator corresponding to the maximal-spin (ferromagnetic) state of the XXX_1 spin chain. The energy of more general rotating and pulsating strings also happens to scale linearly with both the spin and the oscillation number. Such solutions should be dual to other lower-spin states of the spin chain, with the anti-ferromagnetic ground state presumably corresponding to the string pulsating in two planes with no rotation.