Spiky strings in the SL(2) Bethe Ansatz

Abstract

We study spiky strings in the context of the SL(2) Bethe ansatz equations. We find an asymmetric distribution of Bethe roots along one cut that determines the all loop anomalous dimension at leading and subleading orders in a large S expansion. At leading order in strong coupling (large lambda) we obtain that the energy of such states is given, in terms of the spin S and the number of spikes n by E-S=n sqrt{lambda}/(2 pi) (ln 16 pi S/(n sqrt{lambda})+ ln sin (pi/n) - 1)+ O(ln S/S). This result matches perfectly the same expansion obtained from the known spiky string classical solution. We then discuss a two cut spiky string Bethe root distribution at one-loop in the SL(2) Bethe ansatz. In this case we find a limit where n goes to infinity, keeping (E+S)/n^2, (E-S)/n, J/n fixed. This is the one loop version of a limit previously considered in the context of the string classical solutions in AdS5 x S5. In that case it was related to a string solution in the AdS pp-wave background.

32 pages, 6 figures; v2: minor corrections, references added; v3: minor corrections

References in corpus (24)

• Comments on operators with large spin
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Complete 1-loop test of AdS/CFT
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Solitons and AdS String Solutions
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Moduli Dynamics of AdS_3 Strings
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Scaling function in AdS/CFT from the O(6) sigma model
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Quantum corrections to energy of short spinning string in AdS5
• The virtual scaling function of AdS/CFT
• Spiky Strings and Spin Chains
• The integrable O(6) model and the correspondence: checks and predictions
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• A Spin Chain from String Theory

Cited by in corpus (14)

• Exciting the GKP string at any coupling
• Spiky strings in Bethe Ansatz at strong coupling
• Semiclassical rigid strings with two spins in AdS_5
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• From weak coupling to spinning strings
• Multi-spike strings in $Ad{S}_3$ with mixed three-form fluxes
• On N-spike strings in conformal gauge with NS-NS fluxes
• On the dressing phase in the SL(2) Bethe Ansatz
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$
• Generalised scaling at subleading order
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux
• Operator with large spin and spinning D3-brane
• Spiky Strings with Two Spins in AdS5
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux