TY - JOUR

T1 - More on supersymmetric and 2d analogs of the SYK model

AU - Murugan, Jeff

AU - Stanford, Douglas

AU - Witten, Edward

N1 - Funding Information:
Open Access, ©c The Authors. Article funded by SCOAP3.
Publisher Copyright:
© 2017, The Author(s).

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

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U2 - 10.1007/JHEP08(2017)146

DO - 10.1007/JHEP08(2017)146

M3 - Article

AN - SCOPUS:85028735110

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 146

ER -