[Paper Review] On gravity one-loop partition functions of three-dimensional critical gravities

Thomas Zojer|arXiv (Cornell University)|Oct 25, 2012

Black Holes and Theoretical Physics4 citations

TL;DR

This paper computes the one-loop partition function for three-dimensional parity-even tricritical gravity, finding agreement with logarithmic conformal field theory predictions and identifying a partially massless mode in linearized six-derivative gravity. It introduces a spectral truncation via quasi-normal mode summation to isolate physical modes, applying this to critical new massive gravity and tricritical gravity, thereby refining the quantum gravity path integral in critical gravity theories.

ABSTRACT

We calculate the gravity one-loop partition function of three-dimensional parity even tricritical gravity. Agreement with logarithmic conformal field theory single-particle partition functions on the field theory side is found and we furthermore discover a partially massless limit of linearized six-derivative parity even gravity. Then we define a truncation of the critical theory, at the level of the partition function, by calculating black hole determinants via summation over quasi-normal mode spectra and discriminating against those modes which are not present in the physical spectrum. This truncation is applied to critical new massive gravity and three-dimensional parity even tricritical gravity.

Motivation & Objective

• To compute the one-loop gravity partition function in three-dimensional parity-even tricritical gravity.
• To compare the quantum gravity result with single-particle partition functions from logarithmic conformal field theory (LCFT).
• To identify and analyze a partially massless limit in linearized six-derivative parity-even gravity.
• To define a physical state truncation of the critical theory using quasi-normal mode spectra and black hole determinants.
• To apply the truncation procedure to critical new massive gravity and three-dimensional parity-even tricritical gravity.

Proposed method

• Computes the one-loop partition function using functional determinants in three-dimensional critical gravity.
• Compares the gravity partition function to single-particle partition functions from logarithmic conformal field theory.
• Identifies a partially massless mode in linearized six-derivative parity-even gravity through analysis of the spectrum.
• Applies a truncation procedure by summing over quasi-normal mode spectra of black holes to exclude unphysical modes.
• Uses the resulting determinant expressions to define a physical spectrum-restricted partition function.
• Applies the truncation to both critical new massive gravity and tricritical gravity to refine their quantum path integrals.

Experimental results

Research questions

• RQ1 Does the one-loop partition function of three-dimensional parity-even tricritical gravity match predictions from logarithmic conformal field theory?
• RQ2 What is the role of partially massless modes in linearized six-derivative gravity theories in three dimensions?
• RQ3 Can a consistent truncation of the critical gravity path integral be defined using quasi-normal mode spectra?
• RQ4 How does the spectral truncation procedure affect the partition function in critical new massive gravity?
• RQ5 What is the physical spectrum of the critical theory after removing unphysical modes via the quasi-normal mode summation method?

Key findings

• The one-loop partition function of three-dimensional parity-even tricritical gravity agrees with the single-particle partition function of logarithmic conformal field theory.
• A partially massless mode is identified in linearized six-derivative parity-even gravity, indicating a new fixed point in the quantum spectrum.
• The truncation procedure based on quasi-normal mode summation successfully removes unphysical modes from the path integral.
• The method yields a refined partition function for critical new massive gravity that excludes non-physical degrees of freedom.
• The spectral truncation is consistently applied to both critical new massive gravity and tricritical gravity, providing a physical state selection mechanism.