Year: 2006
Type: article
Abstract: We discuss a slow-moving limit of a rigid circular equal-spin solution on $R\ifmmode\times\else\texttimes\fi{}{S}^{3}$. We suggest that the solution with the winding number equal to the total spin approximates the quantum string state dual to the maximal-dimension ``antiferromagnetic'' state of the $SU(2)$ spin chain on the gauge-theory side. An expansion of the string action near this solution leads to a weakly-coupled system of a sine-Gordon model and a free field. We show that a similar effective Hamiltonian appears in a certain continuum limit from the half-filled Hubbard model that was recently suggested to describe the all-order dilatation operator of the dual gauge theory in the $SU(2)$ sector. We also discuss some other slow-string solutions with one spin component in $\mathrm{Ad}{\mathrm{S}}_{5}$ and one in ${S}^{5}$.
Authors: R. Roiban, A. Tirziu, A. A. Tseytlin
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2271753246