Probing Black Hole Thermal Effects in the Dual CFT via Wave Packets

TL;DR

The paper addresses how bulk black-hole thermodynamics in AdS/CFT are imprinted in boundary observables by analyzing bulk wave packets in a BTZ geometry and computing boundary three-point functions of a scalar primary operator. It combines the BDHM dictionary with a conformal transformation from zero temperature to finite temperature (via a cylinder) and a wave-packet smearing to extract $\langle \mathcal{O}(t,x) \rangle_{\beta,\mathrm{wp}}$; the key finding is a temperature-driven exponential damping along the light cone, e.g., $e^{ -\tfrac{4\pi}{\beta}|t| }$, in contrast to the zero-temperature power-law behavior. The energy density, by contrast, factorizes into left- and right-moving components in 2D and does not show thermal suppression along the light cone, highlighting a subtle distinction between bulk causal delays and boundary dissipative signals. Overall, the work provides a concrete, universal mechanism by which bulk thermal physics leaves observable imprints in boundary correlators and offers a computable framework for exploring bulk causal structure holographically.

Abstract

We investigate how the gravitational effects of a black hole manifest themselves as thermal behavior in the dual finite-temperature conformal field theory (CFT). In the holographic framework of AdS/CFT, we analyze a wave packet propagating into a black hole geometry in the bulk by computing three-point functions of a scalar primary operator in the boundary CFT. Our setup captures thermal signatures such as exponential damping of the expectation value, which are absent at zero-temperature. This provides a concrete and analytically tractable example of how black hole physics can be probed from the CFT side.

Figures (8)

• Figure 1: $u_1$-integration contour.
• Figure 2: Profile of $\langle \mathcal{O}(t,x)\rangle_{0,\mathrm{wp}}$ given by \ref{['expO0']} for $a=0.15, p_u =10, p_v = 25, \epsilon= 0.1$. The contribution from the fourth term, which spreads spatially, is neglected. The shockwave-induced contributions decay as a power law along the light cone at zero-temperature.
• Figure 3: The integration contour and the locations of the poles at finite temperature. The blue dots represent the additional poles that emerge at finite temperature, forming an infinite series along the imaginary axis with a separation of $\beta$.
• Figure 4: A wave packet propagating from the origin on the boundary into the bulk, and the associated spherically symmetric shockwave.
• Figure 5: Profile of $\langle\mathcal{O}(t,x) \rangle_{\beta,\mathrm{wp}}$ given by \ref{['evo']} for $a=0.15, p_u =10, p_v = 25, \beta = 3, \epsilon = 0.1$. The contribution from the fourth term, which spreads spatially, is neglected. Shockwave-induced contributions decay exponentially along the light cone at finite temperature. In the high-temperature regime with $\beta p_u \sim \mathcal{O}(1)$, the decay is excessively rapid. For this reason, we set $\beta=3$ in the present plot.