Quantization-scheme-Independent Energy and Its Implications for Holographic Bounds

TL;DR

This paper introduces a quantization-scheme-independent energy concept in holography, ensuring the universal validity of key inequalities like the Penrose inequality and complexity bounds across different quantization choices.

Contribution

It proposes a modified total energy in holographic duality that remains unaffected by quantization schemes, restoring the universality of several holographic inequalities.

Findings

The new energy concept is independent of quantization schemes.

Restores validity of holographic inequalities universally.

Applicable to generalized free scalar field theories.

Abstract

In holographic duality, the total energy of the dual field theory is obtained from the holographic renormalization, which depends not only on the bulk geometry but also on the choice of quantization schemes. We point out that the validity of several widely studied holographic inequalities -- including the AdS Penrose inequality, the late-time bound on entanglement entropy growth, and the growth-rate limits of CV and CA complexities -- depends on the choice of quantization schemes. Motivated by this issue, we introduce a modified total energy, which is still computed via holographic renormalization but the final value is independent of the choice of quantization schemes. We verify that this new ``total energy'' restores all these bounds to universal validity in the model of generalized free scalar field theory. Our results suggest that our modified total energy provides a more robust notion of energy when we talk about above inequalities in holographic settings.