Supergravity, D-brane Probes and thermal super Yang-Mills: a comparison
E. Kiritsis
TL;DR
The paper investigates a D3-brane probe in finite-temperature AdS/CFT to compare supergravity predictions for the probe's worldvolume couplings with perturbative thermal Yang–Mills results. It shows that in the regime $u \gg T$, the strong-coupling (supergravity) effective action aligns with perturbative YM expectations, providing a perturbative test of Maldacena's conjecture; it further derives running electric and magnetic couplings $\lambda_e(T,u)$ and $\lambda_m(T,u)$ from the supergravity background. The work predicts a leading $T^8/u^4$ behavior for the probe potential at large Higgs vev, with the perturbative one-loop contribution exponentially suppressed, and identifies the three-loop term as the first nontrivial correction, consistent with the holographic result. Additionally, it discusses how the emergent worldvolume dynamics yield a field-dependent speed of light and explores cosmological implications, including a suppressed induced cosmological constant on a brane-world and potential inflationary alternatives.
Abstract
A D3-brane probe in the context of AdS/CFT correspondence at finite temperature is considered. The supergravity predictions for the physical effective couplings of the world-volume gauge theory of the probe brane are compared to those calculated in one-loop perturbation theory in the thermal gauge theory. It is argued that when the Higgs expectation value is much larger than the temperature, the supergravity result must agree with perturbative thermal Yang-Mills. This provides a perturbative test of the Maldacena conjecture. Predictions for the running electric and magnetic effective couplings, beyond perturbation theory are also obtained. Phenomenological applications for universe-branes are discussed. In particular mechanisms are suggested for reducing the induced cosmological constant and naturally obtaining a varying speed of light and a consequent inflation on the universe brane.