Proper time to singularity and thermal correlators

Abstract

We study certain higher point thermal correlators of heavy and light scalar primaries in a holographic CFT. Assuming simple self-interactions and couplings of the scalars in the bulk theory, we show that the thermal correlators contain a signature of the proper time to singularity from the horizon. The key idea is to use WKB approximations for the propagators and evaluate the bulk integrals using saddle point method.

Figures (6)

• Figure 1: Witten diagram for the $n$-point function of $\mathcal{O}_{\phi}$ being sourced holographically by a self-interaction term of the dual scalar. The interaction vertex has been marked and the bulk point is integrated over the exterior region. The $\phi$ propagators are denoted by solid lines. Momenta carried by the propagators are indicated and are small in the sense that they do not scale by the mass of the heavy scalar.
• Figure 2: The steepest descent contours for the exponent in \ref{['SDA 3']} with $n = 4$.
• Figure 3: Witten diagram for the heavy-light correlator of primaries $\mathcal{O}_{\phi}$ and $\mathcal{O}_{\chi}$ being sourced holographically by an exchange coupling between the dual scalars. The interaction vertex has been marked and the bulk point is integrated over the exterior region. The $\phi$ propagators are denoted by solid lines while the $\chi$ propagators are denoted by dashed lines. Momenta carried by the propagators are indicated and are small in the sense that they do not scale by the mass of the heavy scalar.
• Figure 4: Witten diagram for the $n-1$-point function of $\mathcal{O}_{\phi}$ being sourced holographically by the self-interaction and the Weyl squared coupling of the dual scalar. The two bulk interaction vertices have been marked separately and both bulk points are integrated over the entire exterior region. The $\phi$ propagators are denoted by solid lines. The momenta carried by the propagators are indicated and are small in the sense that they do not scale by the mass of the heavy scalar.
• Figure 5: Witten diagram for heavy-light correlator being sourced holographically by bulk couplings between the dual fields and the Weyl squared coupling of the heavy scalar. The two bulk interaction vertices have been marked separately and both the bulk points are integrated over the entire exterior region. Solid lines denote propagators for the heavy scalar, $\phi$, and dashed ones are for the light scalar, $\chi$. The momenta carried by the propagators are indicated and are small in the sense that they do not scale by the mass of the heavy scalar.