Exact Results in Extended Holography

• Applicant: Dr. Stijn van Tongeren
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 397115979

• Final Report Year: 2025

Final Report Abstract

The aims of this project are centred on integrability in AdS/CFT, ultimately motivated by one of the biggest challenges of modern theoretical physics: to understand the finite coupling behaviour of quantum field theories. The idea is to use the holographic principle to gain insight on this question from a different, gravitational angle, studying maximally supersymmetric Yang-Mills theory (SYM), and its gravitational dual model, string theory in an anti-de Sitter spacetime, in the framework of the AdS/CFT correspondence. In the limit where the coupling between strings goes to zero, this leaves the dynamics of a single string, dual to SYM in the so-called planar limit. While the theories remain highly nontrivial in this limit, they become integrable, making it possible to do exact computations, and precision tests of holography. In this project we focused our attention on deformations of the above string and SYM, breaking some or all of their maximal (super)symmetry, resulting in a broad landscape of theories with a rich spectrum of observables. On the string side we considered Yang-Baxter deformations, which by construction preserve integrability at the classical level, aiming to understand their effect on the quantum theory. Here we constructed Yang-Baxter deformations of the flat space string, as a helpful toy model for the AdS string, where we were able to explicitly quantize certain models and match their spectra with the effects of expected deformations of the integrable structure. We also computed S matrices for various deformations of the AdS strings, matching them with algebraic expectations based on the deformation operators. On the gauge theory (SYM) side, there was a conjecture that the duals of Yang-Baxter strings were given by SYM on noncommutative spacetimes. This project pursued this conjecture successfully, constructing a large number of these noncommutative theories, and computing observables in some of them, using a map to deformed integrable spin chains. This provides the first detailed quantitative test of (integrability) in holography, in the noncommutative setting. Going beyond the scope of the original proposal, in this project we also studied two further timely topics: providing an integrable coset model description of non-relativistic strings, and highlighting the relationship between TTbar deformations of strings and so-called TsT transformations, indirectly linking back to Yang-Baxter deformations. In addition to the scientific results achieved, as part of this project we organized the successful 2022 edition of the “Integrability, Dualities and Deformations” conference, with over 75 participants.

Publications

• Unimodular jordanian deformations of integrable superstrings. SciPost Physics, 7(1).
  van Tongeren, Stijn
  
• Lie algebra expansion and integrability in superstring Sigma-models. Journal of High Energy Physics, 2020(7).
  Fontanella, Andrea & Romano, Luca
  
• The twisted story of worldsheet scattering in η-deformed AdS5 × S5. Journal of High Energy Physics, 2020(12).
  Seibold, Fiona K.; van Tongeren, Stijn J. & Zimmermann, Yannik
  
• TT deformations as TsT transformations. Physical Review D, 101(6).
  Sfondrini, Alessandro & van Tongeren, Stijn J.
  
• On quantum deformations of AdS3 × S3 × T4 and mirror duality. Journal of High Energy Physics, 2021(9).
  Seibold, Fiona K.; van Tongeren, Stijn J. & Zimmermann, Yannik
  
• Classical string solutions in non-relativistic AdS 5 × S 5 : closed and twisted sectors. Journal of Physics A: Mathematical and Theoretical, 55(8), 085401.
  Fontanella, Andrea & Nieto García, Juan Miguel
  
• Coset space actions for nonrelativistic strings. Journal of High Energy Physics, 2022(6).
  Fontanella, Andrea & van Tongeren, Stijn J.
  
• Do Drinfeld twists of AdS5×S5 A d S 5 × S 5 survive light-cone quantization?. SciPost Physics Core, 5(2).
  van Tongeren, Stijn & Zimmermann, Yannik
  
• Yang-Baxter deformations of the flat space string. Physics Letters B, 835, 137499.
  Idiab, Khalil & van Tongeren, Stijn J.
  
• Gauge theory on twist-noncommutative spaces. Journal of High Energy Physics, 2023(12).
  Meier, Tim & van Tongeren, Stijn J.
  
• Ground state energy of twisted AdS3 × S3 × T4 superstring and the TBA. Journal of High Energy Physics, 2023(9).
  Frolov, Sergey; Pribytok, Anton & Sfondrini, Alessandro
  
• Light-cone gauge in non-relativistic AdS5×S5 string theory. Journal of High Energy Physics, 2023(11).
  Fontanella, Andrea & Nieto García, Juan Miguel
  
• Quadratic Twist-Noncommutative Gauge Theory. Physical Review Letters, 131(12).
  Meier, Tim & van Tongeren, Stijn J.
  
• On exactly solvable Yang-Baxter models and enhanced symmetries. SciPost Physics, 17(4).
  Idiab, Khalil & van Tongeren, Stijn Jurrien
  
• Integrable deformations of the flat space sigma model. Physica Scripta, 100(2), 025211.
  Idiab, Khalil