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On complexity growth in massive gravity theories, the effects of chirality and more

Mahdis Ghodrati

TL;DR

The paper analyzes Hawking-Page type phase transitions and thermodynamic properties across BHT/New Massive Gravity theories, including AdS3 and warped AdS3 geometries, BTZ-like solutions, Gödel and hairy black holes. It develops and applies conserved-charge methods (ADT and SL(2,R) reduction) to compute masses, angular momenta, entropies, and free energies across multiple ensembles, enabling detailed phase diagrams and stability analyses. It also extends the holographic dictionary to warped geometries by adapting modular techniques and investigates inner-horizon thermodynamics and WCFT entanglement entropy, revealing consistency with WCFT data and the impact of warping on holographic quantities. Overall, the work highlights how higher-curvature terms and warping reshape phase structure, dual WCFT data, and entanglement properties, offering insight into holography beyond AdS3.

Abstract

To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter $μ$, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped CFTs in the Tensor Network Renormalization picture.

On complexity growth in massive gravity theories, the effects of chirality and more

TL;DR

The paper analyzes Hawking-Page type phase transitions and thermodynamic properties across BHT/New Massive Gravity theories, including AdS3 and warped AdS3 geometries, BTZ-like solutions, Gödel and hairy black holes. It develops and applies conserved-charge methods (ADT and SL(2,R) reduction) to compute masses, angular momenta, entropies, and free energies across multiple ensembles, enabling detailed phase diagrams and stability analyses. It also extends the holographic dictionary to warped geometries by adapting modular techniques and investigates inner-horizon thermodynamics and WCFT entanglement entropy, revealing consistency with WCFT data and the impact of warping on holographic quantities. Overall, the work highlights how higher-curvature terms and warping reshape phase structure, dual WCFT data, and entanglement properties, offering insight into holography beyond AdS3.

Abstract

To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter , which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped CFTs in the Tensor Network Renormalization picture.

Paper Structure

This paper contains 18 sections, 118 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Bergshoeff-Hohm-Townsend Theory
  3. Review of calculating conserved charges in BHT
  4. The $SL(2,R)$ reduction method
  5. Examples of conserved charges of BHT solutions
  6. Phase transitions of $\text{AdS}_3$ solution
  7. The stability conditions
  8. Phase diagrams
  9. Phase transitions of warped $\text{AdS}_3$ solution in quadratic ensemble
  10. Gödel space-time
  11. Space-like warped BTZ black hole
  12. The free energies and phase diagrams
  13. Phase diagram of warped $\text{AdS}_3$ solution in grand canonical ensemble
  14. local stability
  15. Phase diagram of the hairy black hole
  16. ...and 3 more sections

Figures (11)

  • Figure 1: $m=1.05$.
  • Figure 2: $m=10$.
  • Figure 3: The plot of cosmological constant, $\Lambda$ vs. $-\sqrt{\frac{3}{20}}<\nu< \sqrt{\frac{3}{20}}$.
  • Figure 4: The central charge of NMG vs. $\nu$.
  • Figure 5: The phase diagram for $\nu=0.387$.
  • ...and 6 more figures