Exact approaches on the string worldsheet

Demulder, Saskia; Driezen, Sibylle; Knighton, Bob; Oling, Gerben; Retore, Ana L; Seibold, Fiona K; Sfondrini, Alessandro; Yan, Ziqi

Abstract

We review different exact approaches to string theory. In the context of the Green–Schwarz superstring, we discuss the action in curved backgrounds and its supercoset formulation, with particular attention to superstring backgrounds of the AdS3 type supported by both Ramond–Ramond and Neveu–Schwarz–Neveu–Schwarz fluxes. This is the basis for the discussion of classical integrability, of worldsheet-scattering factorisation in the uniform lightcone gauge, and eventually of the string spectrum through the mirror thermodynamic Bethe ansatz, which for AdS3 backgrounds was only derived and analysed very recently. We then illustrate some aspects of the Ramond–Neveu–Schwarz string, and introduce the formalism of Berkovits–Vafa–Witten, which has seen very recent applications to AdS3 physics, which we also briefly review. Finally, we present the relation between M-theory in the discrete lightcone quantisation and decoupling limits of string theory that exhibit non-relativistic behaviors, highlighting the connection with integrable TT¯ deformations, as well as the relation between spin-matrix theory and Landau–Lifshitz models. This review is based on lectures given at the Young Researchers Integrability School and Workshop 2022 ‘Taming the string worldsheet’ at NORDITA, Stockholm.

Citation

Demulder, S., Driezen, S., Knighton, B., Oling, G., Retore, A. L., Seibold, F. K., Sfondrini, A., & Yan, Z. (2024). Exact approaches on the string worldsheet. Journal of Physics A: Mathematical and Theoretical, 57(42), Article 423001. https://doi.org/10.1088/1751-8121/ad72be

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2024
• Online Publication Date: Sep 30, 2024
• Publication Date: Nov 8, 2024
• Deposit Date: Oct 9, 2024
• Publicly Available Date: Oct 9, 2024
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 57
• Issue: 42
• Article Number: 423001
• DOI: https://doi.org/10.1088/1751-8121/ad72be
• Keywords: worldsheet S matrix, hybrid superstring, non-relativistic strings, Green–Schwarz superstring, mirror thermodynamic Bethe ansatz, integrable sigma models, AdS3/CFT2
• Public URL: https://durham-repository.worktribe.com/output/2948815