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We developed a new formula for calculating the free energy of odd-dimensional conformal field theories (CFTs) on squashed spheres. This method simplifies calculations for holographic CFTs and reveals universal properties of (2+1)-dimensional CFTs.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • String Theory

Background:

  • Conformal Field Theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • Calculating the free energy of CFTs on curved manifolds, like squashed spheres, is a key challenge.
  • Holographic duality provides a powerful tool to study CFTs via gravitational theories.

Purpose of the Study:

  • To propose a novel formula for computing the free energy of odd-dimensional CFTs on squashed spheres.
  • To explore the connection between the free energy and the bulk gravitational theory in holographic settings.
  • To investigate universal properties of (2+1)-dimensional CFTs related to their stress tensor.

Main Methods:

  • Development of a new formula for free energy calculation in holographic CFTs.
  • Utilizing higher-curvature gravities with second-order linearized equations of motion.
  • Evaluation of bulk Lagrangians on auxiliary anti-de Sitter (AdS) spaces.
  • Analysis of AdS vacua generating functional for stress tensor correlation functions.
  • Combination of holographic results with free-field numerical calculations.

Main Results:

  • A proposed formula for the free energy of holographic CFTs on squashed spheres.
  • Demonstration that the formula simplifies calculations compared to standard on-shell action methods.
  • Identification of a connection between the free energy formula and AdS vacua, suggesting a generating functional.
  • Conjecture that the subleading term in the free energy expansion for (2+1)-dimensional CFTs is universally controlled by the stress-tensor three-point function charge t_{4}.

Conclusions:

  • The proposed formula offers an efficient method for computing free energy in holographic CFTs.
  • The study provides insights into the structure of holographic theories and their boundary CFTs.
  • A universal feature of (2+1)-dimensional CFTs concerning their free energy expansion is identified.