Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT

By D. Hofman. 2009

260 citations recorded by the source corpus.

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 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b72240048f4e4ff1ad766a142d6d3d13d52194c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. Aninda Sinha
3. T. Faulkner
4. M. Paulos
5. M. Smolkin
6. A. Singh
7. T. Takayanagi
8. S. Cremonini

In Nuclear and High Energy Physics

1. R. Myers
2. Aninda Sinha
3. T. Faulkner
4. Thomas Hartman
5. J. Maldacena
6. T. Takayanagi
7. M. Paulos
8. A. Singh

Citations in the corpus

• Holographic entanglement entropy in Lovelock gravities (2011, background): “(Work which uses higher derivative gravitational theories to study unitarity constraints in CFTs includes [12-25].”
• Analytical study on holographic superconductors in external magnetic field (2010, methodology): “The Gauss-Bonnet coupling constant is constrained simultaneously by the positivity of the energy constraints in conformal field theories [ 42 ] and causality in their dual gravity description [43].”
• Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, methodology): “Since then, there have been several attempts at a proof of the HM bounds with varying levels of success [35,40,41].”
• The Shear Viscosity to Entropy Ratio: A Status Report (2011, background): “Exactly the same constraint arises by requiring “positivity of energy” measured by a detector in the plasma [74].”
• Black holes in quasi-topological gravity (2010, background): “, requiring that the boundary theory is causal, imposes much more stringent constraints on the GB coupling [5, 6] − 7 36 ≤ λ ≤ 9 100 .”
• On graviton non-gaussianities during inflation (2011, background): “22 There are bounds similar to the ones derived in [32] for the parity breaking and parity conserving coefficients that appear in a three point function.”
• Emergent spacetime and holographic CFTs (2011, unknown): “For such an analysis it might be important to also analyze the consistency of the theory at finite temperature, as was partially done in [107], [108], [109], [110].”
• Holographic studies of quasi-topological gravity (2010, background): “Of course, this agreement for GB gravity was previously noted [11, 15, 12].”
• Causality of holographic hydrodynamics (2009, methodology): “We would like to thank Diego Hofman for sharing an early draft of [30] with us.”
• Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity (2009, methodology): “We complete the discussion initiated in [ 18 ], showing explicitly that the lower bounds can be obtained from scalar perturbations.”
• Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “Physically, the arguments for such a refined bound involve demonstrating that violations of these bounds would lead, in a wide class of theories, either to violations of causality in the field theory [10, 362] or to violations of the positivity of energy [363]; in fact, these two pathologies are int”
• Causality constraints in conformal field theory (2015, background): “This was first shown for c2 outside a certain range [3, 4], and more recently extended to any non-zero value of c2 by Camanho, Edelstein, Maldacena, and Zhiboedov (CEMZ) [6].”
• AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound (2009, background): “The understanding of this correspondence is at present somewhat incomplete although it was argued in [ 5 ]”