SCALE INVARIANCE VS CONFORMAL INVARIANCE FROM HOLOGRAPHY

2010 ◽  
Vol 25 (26) ◽  
pp. 4849-4873 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Conformal Invariance ◽  
Scale Invariance ◽  
Unsolved Problem ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum Field ◽  
Gravitational Theories ◽  
Higher Dimensional ◽  
Holographic Approach

The relation between scale invariance and conformal invariance is a subtle but important unsolved problem in the quantum field theory. We study a holographic approach to this problem and show that the null energy condition in the bulk effective gravitational theories guarantees the equivalence between the scale invariance and conformal invariance of the boundary theories. We also investigate the higher-dimensional compactification, where the warping can generate additional possible violation of the conformal invariance. Our discussion is applicable in any dimension, and suggests a generalization of Zamolodchikov–Polchinski theorem that states the equivalence in (1+1) dimension from the purely field theory viewpoint.

scholarly journals Macroscopic traversable wormholes with zero tidal forces inspired by noncommutative geometry

2015 ◽  
Vol 24 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Peter K. F. Kuhfittig
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Energy Density ◽  
Noncommutative Geometry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum Field ◽  
Tidal Forces ◽  
Traversable Wormholes ◽  
Asymptotic Flatness

This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum-field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies the usual requirements, including asymptotic flatness.

scholarly journals Classification of quantum states based on the null energy condition

2021 ◽  
Vol 36 (25) ◽  
pp. 2150183
Author(s):  
Susobhan Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Coherent States ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum States ◽  
Quantum Field ◽  
Theory Of Relativity ◽  
General Theory Of Relativity

Violation of the null energy condition plays an important role both in the general theory of relativity and quantum field theory in curved spacetimes. Over the years, it has been shown that the violation of the null energy condition leads to instability and violation of causality. In quantum field theory, violation of the energy condition also depends on the quantum states apart from the geometry of curved spacetime. Hence, the quantum effects play an important role in the violation of the null energy condition. We show that the set of all the coherent states does not violate the null energy condition. Further, we also show that under certain conditions, the null energy condition is violated either by a pure state or a mixed state. Furthermore, the dynamical violation of the null energy condition by the quantum states is also discussed here.

scholarly journals Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 171
Author(s):  
Folkert Kuipers ◽  
Xavier Calmet
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Effective Field Theory ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Effective Field ◽  
Second Order ◽  
Jordan Frame ◽  
Singularity Theorems ◽  
Massive Spin

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

scholarly journals Higher-dimensional evolving wormholes satisfying the null energy condition

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
Mahdi Kord Zangeneh ◽  
Francisco S. N. Lobo ◽  
Nematollah Riazi
Keyword(s):  
Energy Condition ◽  
Null Energy Condition ◽  
Higher Dimensional

scholarly journals New gedanken experiment on higher-dimensional asymptotically AdS Reissner–Nordström black hole

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Ming Zhang ◽  
Jie Jiang
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Order Approximation ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Matter Field ◽  
Second Order ◽  
Field Perturbation ◽  
Higher Dimensional ◽  
Dynamical Quantity

AbstractViewing the negative cosmological constant as a dynamical quantity derived from the matter field, we study the weak cosmic censorship conjecture for the higher-dimensional asymptotically AdS Reissner–Nordström black hole. To this end, using the stability assumption of the matter field perturbation and the null energy condition of the matter field, we first derive the first-order and second-order perturbation inequalities containing the variable cosmological constant and its conjugate quantity for the black hole. We prove that the higher-dimensional RN-AdS black hole cannot be destroyed under a second-order approximation of the matter field perturbation process.

scholarly journals ON ϵ-CONJECTURE IN a-THEOREM

2012 ◽  
Vol 27 (05) ◽  
pp. 1250029 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Strong Evidence ◽  
Conformal Invariance ◽  
Scale Invariance ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Complete Proof ◽  
Four Dimensions

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the ϵ-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimensions. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories.

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