Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT (0907.1625v2)

Abstract: In this note we discuss the relation between the constraints imposed by causality in the bulk of $AdS$ and the condition of positivity of the energy measured in ideal calorimeters in a collider experiment in the dual CFT. We first extend the analysis in the literature and recover all bounds imposed by causality of the boundary theory in the bulk dynamics for all polarizations of the graviton and the gauge boson field. These results translate to specific bounds for the ratio of central charges $\frac{a}{c}$ in the dual CFT, already found by analyzing the energy one point function. Then, we generalize this discussion and we study shock wave backgrounds in which we make manifest the relation between causality in the bulk and the three point function in the dual field theory. We remark that particular care has to be given to the exponentiation procedure of the three point function when solving the classical equations of motion in the higher gravity theory, as it is not clear that every theory will present causality problems. Finally, we present a field theoretic argument explaining the positivity of energy condition in any UV complete QFT.

• The paper investigates how bulk causality in AdS leads to explicit bounds on the a/c ratio in dual conformal field theories.
• The study derives central charge limits from energy correlation functions that secure positivity of energy in collider setups.
• The findings reveal that enforcing causality constraints universally refines permissible parameters for UV complete quantum field theories.

Overview of Higher Derivative Gravity, Causality, and Positivity of Energy in QFT

The paper "Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT" addresses crucial aspects of quantum field theories (QFTs) and their correspondence with gravitational theories, specifically focusing on higher derivative gravity models. Through the lens of the AdS/CFT correspondence, the paper explores the constraints imposed by causality in the anti-de Sitter (AdS) space and how these relate to the positivity of energy conditions in the dual conformal field theories (CFTs).

Summary of Key Contributions

1. Causality and Energy Positivity: The paper investigates the relationship between constraints imposed by bulk causality in AdS and the positivity of energy as measured by calorimeters in a collider setup in the CFT. It extends previous analyses to encompass all polarizations of gravitons and gauge bosons, showing that these requirements enforce specific bounds on the ratio of central charges $\frac{a}{c}$ in the dual CFT.
2. Central Charge Bounds: The paper presents explicit bounds derived from causality, linking them to $\frac{a}{c}$ in the dual gauge theory. These bounds coincide with those necessary to maintain the positivity of energy conditions, already analyzed in the context of energy correlation functions.
3. Gravity Duals and Energy Correlation Functions: The paper provides a detailed investigation of gravity duals of energy correlation functions, particularly focusing on shock wave backgrounds. It outlines how gravitational perturbations align with constraints deduced from collider physics analysis of conformal field theories, establishing a direct correspondence between theoretical predictions and phenomenological constraints.
4. Positivity of Energy in CFTs: An argument is formulated for the positivity of energy in any UV complete quantum field theory. This argument extends beyond strongly coupled or supersymmetric theories, suggesting a universal applicability across all UV complete QFTs.

Numerical and Theoretical Implications

The findings yield significant implications both practically and theoretically. Practically, they ensure that any proposed gravity action that violates causality constraints could likely yield non-causal behavior in dual CFTs experimentally. This insight is vital for theoretical physicists working on beyond-standard-model physics, potentially impacting approaches to quantum gravity and string theory.

Theoretically, the investigation extends the understanding of how higher derivative terms influence the dual description of field theories. The deduced bounds suggest that adhering to energy positivity and causality constraints refines the permissible parameter spaces of QFTs and their gravitational duals.

Speculation on Future Developments in AI and Theoretical Physics

The methodologies utilized in this paper could inspire future AI advancements in simulating higher derivative gravitational models, optimizing calculations for field theories with complex boundary conditions. Additionally, these findings might guide researchers developing AI algorithms for data analysis from collider experiments by providing stringent theoretical constraints rooted in fundamental physics principles.

Conclusion

This paper addresses pivotal aspects of the confluence between gravitational theories with higher derivatives and dual conformal field theories, focusing on causality and positivity of energy conditions. The work substantiates the interconnection between theoretical predictions and phenomenological constraints, contributing to the deeper comprehension of the AdS/CFT correspondence and its implications in theoretical physics. The results are influential for ensuring the causality of gravitational theories and aligning them with observable phenomena in collider experiments, highlighting the profound link between geometry and quantum field theory in the fabric of nature.