Slow-string limit and "antiferromagnetic" state in AdS/CFT

Abstract

We discuss a slow-moving limit of a rigid circular equal-spin solution on R x 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 AdS_5 and one in S^5.

32 pages, Latex v2: one footnote and references added

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• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Infinite spin limit of semiclassical string states
• Single spike solutions for strings on S2 and S3
• Spiky Strings, Giant Magnons and beta-deformations
• Large Winding Sector of AdS/CFT
• Scattering of single spikes
• On the anatomy of multi-spin magnon and single spike string solutions
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Massless sector of AdS_3 superstrings: a geometric interpretation
• On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
• Aspects of Integrability in AdS/CFT Duality
• Bethe Ansatz solutions for highest states in $\mathcal{N}=4$ SYM and AdS/CFT duality
• Wilson loops T-dual to Short Strings
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• Giant Spinons
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems
• The Omega-Infinity Limit of Single Spikes
• AdS/CFT duality at strong coupling