Generalized dualities relating gravitational theories in 4-dimensional Anti-deSitter space with 3-dimensional conformal field theories

• Applicant: Professor Dr. Olaf Hohm
• Co-Applicant: Professor Dr. Daniel Grumiller
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 212628803

• Final Report Year: 2016

Final Report Abstract

The objective of this DFG project was to investigate generalized AdS/CFT dualities, for which the bulk theory is unconventional: either a version of massive or higherderivative gravity or a higher-spin gravity as constructed by Vasiliev. In relation to higher-derivative gravity, in 2013–2014 I showed together with Bergshoeff, Townsend and others that the infamous ‘bulk-boundary conflict’ present in 3D theories (such as topologically massive gravity and new massive gravity) can be avoided by introducing Chern-Simons-like theories with multiple frame fields. This resolved a problem that has been prominent at least since the 2008 ‘chiral gravity’ proposal by Strominger and collaborators. In addition, Sachs and Ponomarev published important articles on higher-spin gravity, in particular in relation to the conjectured duality to 3D O(N) vector models. Specifically, Sachs made relevant contributions to the idea of deriving the correspondence from first principles by reinterpreting the Vasiliev equations as renormalization group equations for the boundary theory. Ponomarev and collaborators added to the ongoing quest of verifying and understanding this correspondence, for instance of how to reconstruct the bulk interactions holographically.

Publications

• On the Hamiltonian form of 3D massive gravity, Phys. Rev. D. 86. 084035, 2013
  O. H., A. Routh, P. K. Townsend, B. Zhang
  (See online at https://doi.org/10.1103/PhysRevD.86.084035)
• Zwei-Dreibein Gravity: A Two-Frame-Field Model of 3D Massive Gravity, Phys. Rev. Lett. 111, no. 11, 111102, 2013, Erratum: Phys. Rev. Lett. 111, no. 25, 259902, 2013
  E. A. Bergshoeff, S. de Haan, O. H., W. Merbis and P. K. Townsend
  
• Higher spin versus renormalization group equations, Phys. Rev. D 90, no. 8, 085003, 2014
  I. Sachs
  (See online at https://doi.org/10.1103/PhysRevD.90.085003)
• Minimal Massive 3D Gravity, Class. Quant. Grav. 31, 145008, 2014
  E. Bergshoeff, O. H., W. Merbis, A. J. Routh and P. K. Townsend
  
• Bulk quartic vertices from boundary four-point correlators, Proceedings of “International Workshop on Higher Spin Gauge Theories”, Singapore, 2015
  X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight
  
• Chern-Simons-like Gravity Theories, Lect. Notes Phys. 892, 181, 2015
  E. A. Bergshoeff, O. H., W. Merbis, A. J. Routh and P. K. Townsend
  
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory, JHEP 1511, 149, 2015
  X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight
  
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange, JHEP 1503, 170, 2015
  X. Bekaert, J. Erdmenger, D. Ponomarev, C. Sleight