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Higher-Dimensional Fermionic SYK Model in IR Region

Xing Huang, Chen-Te Ma

TL;DR

The paper analyzes the IR properties of a 2D fermionic SYK model with Majorana fermions and a Gaussian-disordered $2q$-body interaction by formulating and solving the large-$N$ Schwinger-Dyson equations, revealing a conformal IR structure with $ riangle=1/q$ and a vanishing spin $s$ (for $q=1$). It computes the OTOC to extract the Lyapunov exponent, finding violations of the chaos bound and, via bootstrap, of the unitarity bound in the IR, pointing to an incomplete IR description that may require UV completion or supersymmetry. The gravitational dual is shown to correspond to AdS$_3$ Einstein gravity with a finite radial cutoff, realized through a double Schwarzian boundary action, linking the IR dynamics to holographic boundary theories. The work also extends the framework to higher dimensions, preserving the same IR structure and offering a route toward UV-complete, holographically flavored generalizations of SYK-like models.

Abstract

We study the 2D fermionic SYK model with Majorana fermions, featuring a quartic kinetic term and a $2q$-body interaction with Gaussian disorder. By minimizing the effective action or solving the SD equation for $q=1$, we determine that the appropriate ansatz involves zero spins. Our computation of the Lyapunov exponent shows violations of chaos and unitarity bounds. The gravitational dual corresponds to AdS$_3$ Einstein gravity with a finite radial cut-off, even if we lose the non-zero spins. We also extend the SYK model to higher dimensions while maintaining a similar SD equation in the IR.

Higher-Dimensional Fermionic SYK Model in IR Region

TL;DR

The paper analyzes the IR properties of a 2D fermionic SYK model with Majorana fermions and a Gaussian-disordered -body interaction by formulating and solving the large- Schwinger-Dyson equations, revealing a conformal IR structure with and a vanishing spin (for ). It computes the OTOC to extract the Lyapunov exponent, finding violations of the chaos bound and, via bootstrap, of the unitarity bound in the IR, pointing to an incomplete IR description that may require UV completion or supersymmetry. The gravitational dual is shown to correspond to AdS Einstein gravity with a finite radial cutoff, realized through a double Schwarzian boundary action, linking the IR dynamics to holographic boundary theories. The work also extends the framework to higher dimensions, preserving the same IR structure and offering a route toward UV-complete, holographically flavored generalizations of SYK-like models.

Abstract

We study the 2D fermionic SYK model with Majorana fermions, featuring a quartic kinetic term and a -body interaction with Gaussian disorder. By minimizing the effective action or solving the SD equation for , we determine that the appropriate ansatz involves zero spins. Our computation of the Lyapunov exponent shows violations of chaos and unitarity bounds. The gravitational dual corresponds to AdS Einstein gravity with a finite radial cut-off, even if we lose the non-zero spins. We also extend the SYK model to higher dimensions while maintaining a similar SD equation in the IR.

Paper Structure

This paper contains 9 sections, 54 equations, 3 figures.

Table of Contents

  1. Introduction
  2. 2D Fermionic SYK Model
  3. Large-$N$ SD Equation
  4. Kernel
  5. Chaos and Unitarity Bounds
  6. Chaos Bound
  7. Unitarity Bound
  8. Gravitational Dual
  9. Higher Dimensions

Figures (3)

  • Figure 1: The derivative of $S\equiv\ln(\bar{G}_+\bar{G}_-)$ for the spin $s$. The $S$ is proportional to the effective action. As we can see, it is neither even nor odd concerning $s$.
  • Figure 2: The Lyapunov exponents for different $q$. The chaos bound is violated for $q\le 6$. The dashed line indicates the chaos bound.
  • Figure 3: The dimensions of the lightest scalars in the spectrum are compared to the shaded allowed region set by the unitarity bound.