The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model

Abstract

The $\text{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten model realises bosonic-string theory in ${\text{AdS}}_3$ with pure Neveu-Schwarz-Neveu-Schwarz flux. We construct an effective action in the semi-classical limit of the model, which corresponds to a $\text{SL}(2,\mathbb{R})$ spin-chain $\sigma$-model. We adopt two complementary points of view. Firstly, we consider the classical action. We identify fast and slow target-space coordinates. We impose a gauge-fixing condition to the former. By expanding the gauge-fixed action in an effective coupling, we obtain the effective action for the slow coordinates. Secondly, we consider the spin chain of the model. We postulate a set of coherent states to express a transition amplitude in the spin chain as a path integral. We observe that the temporal interval is discretised in terms of the step length of the spatial interval. This relationship implies that the Landau-Lifshitz limit of the spin chain involves both intervals. The limit yields a semi-classical path integral over coherent states, wherein we identify the effective action again.

arXiv comment18 pages. v2: Minor corrections and improvements. v3: Minor corrections and improvements. Manuscript corresponds to the published version

References in corpus (37)

• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Multi-spin string solutions in AdS_5 x S^5
• Spin chains and string theory
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• An Introduction to T-Duality in String Theory
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Spiky strings and single trace operators in gauge theories
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Strings on NS-NS Backgrounds as Integrable Deformations
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector
• On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
• The WZNW model on PSU(1,1|2)
• On semiclassical approximation and spinning string vertex operators in AdS_5 x S^5
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Higher Loops Beyond the SU(2) Sector
• Higher spins on AdS${}_3$ from the worldsheet
• Semiclassical strings and AdS/CFT
• Spin chain sigma models with fermions
• Super spin chain coherent state actions and $Ad{S}_5\times S^5$ superstring
• Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Sigma model from SU(1,1|2) spin chain
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• Quantum Coherent String States in AdS_3 and SL(2,R) WZWN Model
• New Coherent String States and Minimal Uncertainty in WZWN Models
• Unification of Gravitation, Gauge Field and Dark Energy
• Long Strings and Symmetric Product Orbifold from the AdS${}_3$ Bethe Equations
• The $SU(2)$ Wess-Zumino-Witten spin chain sigma model

Cited by in corpus (2)

• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Deforming integrable models of AdS${}_3$ strings