More on supersymmetric and 2d analogs of the SYK model

Jeff Murugan, Douglas Stanford, Edward Witten

Research output: Contribution to journalArticlepeer-review

139 Scopus citations


In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d supersymmetric SYK model. We then introduce new bosonic and supersymmetric analogs of SYK in two dimensions. These theories consist of N fields interacting with random q-field interactions. Although models built entirely from bosons appear to be problematic, we find a supersymmetric model that flows to a large N CFT with interaction strength of order one. We derive an integral formula for the four-point function at order 1/N , and use it to compute the central charge, chaos exponent and some anomalous dimensions. We describe a problem that arises if one tries to find a 2d SYK-like CFT with a continuous global symmetry.

Original languageEnglish (US)
Article number146
JournalJournal of High Energy Physics
Issue number8
StatePublished - Aug 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT Correspondence
  • Conformal Field Theory


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