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Quantum-corrected three-dimensional AdS space-time

Jacob C. Thompson, Elizabeth Winstanley

TL;DR

This work investigates quantum backreaction on three-dimensional global AdS space by promoting the classical stress-energy tensor to the renormalized stress-energy tensor (RSET) of a massless conformally coupled scalar in a global thermal state and solving the linearized quantum-corrected Einstein equations. By computing the RSET both via quantum field theory (QFT) and relativistic kinetic theory (RKT), the authors construct static, soliton-like solutions to the LQCEE, characterized by a BTZ-like mass function $m(R)$ and a finite soliton mass $M=\lim_{R\to\infty}m(R)$; explicit expressions are provided for $M$ in both RKT and QFT cases. The RKT result overestimates the QFT result at fixed $\beta$ but provides a simpler high-temperature proxy, and in both approaches the energy density is positive and localized with a regular origin. The findings illustrate how quantum backreaction in a simple AdS setting can yield regular solitons and establish a framework for exploring rotating quantum-corrected solitons in future work.

Abstract

We study quantum-corrected solitons in global, three-dimensional, anti-de Sitter (AdS) space-time. These static solitons have a regular origin and arise as solutions of the linearized quantum-corrected Einstein equations (LQCEE). On the right-hand-side of the LQCEE is the renormalized expectation value of the stress-energy tensor operator for a massless, conformally coupled, quantum scalar field in a nonrotating thermal state, computed in quantum field theory (QFT), or using relativistic kinetic theory (RKT). We calculate the mass of the solitons and compare the results from QFT and RKT.

Quantum-corrected three-dimensional AdS space-time

TL;DR

This work investigates quantum backreaction on three-dimensional global AdS space by promoting the classical stress-energy tensor to the renormalized stress-energy tensor (RSET) of a massless conformally coupled scalar in a global thermal state and solving the linearized quantum-corrected Einstein equations. By computing the RSET both via quantum field theory (QFT) and relativistic kinetic theory (RKT), the authors construct static, soliton-like solutions to the LQCEE, characterized by a BTZ-like mass function and a finite soliton mass ; explicit expressions are provided for in both RKT and QFT cases. The RKT result overestimates the QFT result at fixed but provides a simpler high-temperature proxy, and in both approaches the energy density is positive and localized with a regular origin. The findings illustrate how quantum backreaction in a simple AdS setting can yield regular solitons and establish a framework for exploring rotating quantum-corrected solitons in future work.

Abstract

We study quantum-corrected solitons in global, three-dimensional, anti-de Sitter (AdS) space-time. These static solitons have a regular origin and arise as solutions of the linearized quantum-corrected Einstein equations (LQCEE). On the right-hand-side of the LQCEE is the renormalized expectation value of the stress-energy tensor operator for a massless, conformally coupled, quantum scalar field in a nonrotating thermal state, computed in quantum field theory (QFT), or using relativistic kinetic theory (RKT). We calculate the mass of the solitons and compare the results from QFT and RKT.

Paper Structure

This paper contains 4 sections, 10 equations, 1 figure.

Table of Contents

  1. Introduction
  2. RSET on AdS${}_{3}$
  3. QC AdS${}_{3}$ solitons
  4. Conclusions

Figures (1)

  • Figure 1: Energy density $E=-T_{t}^{t}$ for $\beta \in \{3\pi/4, 5\pi/6, 11\pi/12, \pi \}$ (left) and $\beta \in \{ \pi/6, \pi /4, \pi /3, 5\pi /12 \}$ (middle). QC soliton mass $M$ (\ref{['eq:mass']}) (right) as a function of inverse temperature $\beta$. Dotted lines denote results from RKT, while solid lines are those from QFT. We set the AdS inverse length scale $a=1$.