Spacetime Energy Decreases under World-sheet RG Flow

TL;DR

This paper demonstrates that in certain two-dimensional sigma models, the spacetime energy decreases along the renormalization group flow, aligning with known energy decrease phenomena in tachyon condensation.

Contribution

It establishes a connection between world-sheet RG flow and spacetime energy decrease using the Zamolodchikov c-theorem in asymptotically flat target spaces.

Findings

Spacetime energy decreases from UV to IR fixed points.

The result parallels energy decrease in tachyon condensation.

Uses the c-theorem to relate RG flow to energy changes.

Abstract

We study renormalization group flows in unitary two dimensional sigma models with asymptotically flat target spaces. Applying an infrared cutoff to the target space, we use the Zamolodchikov c-theorem to demonstrate that the target space ADM energy of the UV fixed point is greater than that of the IR fixed point: spacetime energy decreases under world-sheet RG flow. This result mirrors the well understood decrease of spacetime Bondi energy in the time evolution process of tachyon condensation.