Bibliographic Details
| Title: |
The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model |
| Authors: |
Ruiz, Roberto |
| Source: |
Phys. Rev. D 103, 106024 (2021) |
| Publication Year: |
2021 |
| Collection: |
High Energy Physics - Theory |
| Subject Terms: |
High Energy Physics - Theory |
| More Details: |
The $\textrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten model realises bosonic-string theory in $\textrm{AdS}_{3}$ with pure Neveu-Schwarz-Neveu-Schwarz flux. We construct an effective action in the semi-classical limit of the model, which corresponds to a $\textrm{SL}(2,\mathbb{R})$ 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.
Comment: 18 pages. v2: Minor corrections and improvements. v3: Minor corrections and improvements. Manuscript corresponds to the published version |
| Document Type: |
Working Paper |
| DOI: |
10.1103/PhysRevD.103.106024 |
| Access URL: |
http://arxiv.org/abs/2101.12119 |
| Accession Number: |
edsarx.2101.12119 |
| Database: |
arXiv |
