scholarly journals A Rényi quantum null energy condition: proof for free field theories

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mudassir Moosa ◽  
Pratik Rath ◽  
Vincent Paul Su
Keyword(s):  
Relative Entropy ◽  
Free Field ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Field Theories ◽  
Energy Tensor ◽  
Shape Derivative ◽  
Spacetime Dimension ◽  
Positivity Condition ◽  
Stress Energy

Abstract The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy Srel(ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence Sn(ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of Sn(ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.

scholarly journals EXACT SOLUTIONS OF BRANS–DICKE WORMHOLES IN THE PRESENCE OF MATTER

2011 ◽  
Vol 26 (40) ◽  
pp. 3067-3076 ◽  
Author(s):  
NADIEZHDA MONTELONGO GARCIA ◽  
FRANCISCO S. N. LOBO
Keyword(s):  
Scalar Field ◽  
Vacuum Solution ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Exotic Matter ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Normal Matter ◽  
Stress Energy

A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In this work, we find exact wormhole solutions in Brans–Dicke theory where the normal matter threading the wormhole satisfies the null energy condition throughout the geometry. Thus, the latter implies that it is the effective stress–energy tensor containing the scalar field, that plays the role of exotic matter, that is responsible for sustaining the wormhole geometry. More specifically, we consider a zero redshift function and a particular choice for the scalar field and determine the remaining quantities, namely, the stress–energy tensor components and the shape function. The solution found is not asymptotically flat, so that this interior wormhole spacetime needs to be matched to an exterior vacuum solution.

scholarly journals Composite operators in $$ T\overline{T} $$-deformed free QFTs

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Anshuman Dey ◽  
Mikhail Goykhman ◽  
Michael Smolkin
Keyword(s):  
Free Field ◽  
Perturbative Expansion ◽  
Field Theories ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Stress Energy Tensor ◽  
Massless Theory ◽  
Stress Energy ◽  
Perturbative Renormalization ◽  
Massive Theory

Abstract We study perturbative renormalization of the composite operators in the $$ T\overline{T} $$ T T ¯ -deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].

Kerr–Newman black holes cannot be over-charged or over-spun

2018 ◽  
Vol 27 (11) ◽  
pp. 1843003 ◽  
Author(s):  
Robert M. Wald
Keyword(s):  
Black Hole ◽  
Energy Condition ◽  
Finite Size ◽  
Null Energy Condition ◽  
Second Order ◽  
Energy Tensor ◽  
Finite Size Effects ◽  
Stress Energy ◽  
Newman Black Hole ◽  
Self Force

I describe research done in collaboration with J. Sorce showing that one cannot over-charge and/or over-spin an initially slightly nonextremal Kerr–Newman black hole via the type of gedanken experiments proposed by Hubeny and others, assuming that the nonelectromagnetic stress-energy tensor of the matter entering the black hole satisfies the null energy condition. Analysis of such gedanken experiments requires that we calculate all effects on the final mass of the black hole that are second-order in the charge and the angular momentum carried into the black hole. We do so using Lagrangian methods, and our formula for the second-order correction to mass, [Formula: see text], is obtained by generalizing the canonical energy analysis of Hollands and Wald to the Einstein–Maxwell case. Our formula for [Formula: see text] automatically includes all self-force and finite size effects.

scholarly journals Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

2022 ◽  
Author(s):  
Thomas Faulkner ◽  
Stefan Hollands ◽  
Brian Swingle ◽  
Yixu Wang
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Reference State ◽  
Type I ◽  
Von Neumann ◽  
Link Type ◽  
Fixed Reference ◽  
Proof Strategy

AbstractWe prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda $$L_p$$ L p norms. We comment on applications to the quantum null energy condition.

scholarly journals Relative Entropy of Coherent States on General CCR Algebras

2021 ◽  
Author(s):  
Henning Bostelmann ◽  
Daniela Cadamuro ◽  
Simone Del Vecchio
Keyword(s):  
Relative Entropy ◽  
Coherent States ◽  
Regularity Condition ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Boundary Terms ◽  
Ccr Algebra ◽  
Modular Data ◽  
Quasifree State ◽  
Thermal States

AbstractFor a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

scholarly journals On the existence and stability of traversable wormhole solutions in modified theories of gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Oleksii Sokoliuk ◽  
Alexander Baransky
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Traversable Wormhole ◽  
Existence And Stability ◽  
Theories Of Gravity ◽  
The Stability

AbstractWe study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$ f ( R ) = R + a R 2 , power-law $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$ f ( R ) = f 0 R n , log-corrected $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$ f ( R ) = R + α R 2 + β R 2 ln β R theories, and finally on the exponential hybrid metric-Palatini gravity $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$ f ( R ^ ) = ζ ( 1 + e - R ^ Φ ) . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state $$p_t=\omega \rho $$ p t = ω ρ . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

scholarly journals Quantum null energy condition and its (non)saturation in 2d CFTs

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Christian Ecker ◽  
Daniel Grumiller ◽  
Wilke van der Schee ◽  
Shahin Sheikh-Jabbari ◽  
Philipp Stanzer
Keyword(s):  
Central Charge ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Einstein Gravity ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Leading Order ◽  
Conformal Field ◽  
Primary Operator ◽  
Vacuum Solutions

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions of AdS_33 Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT_22 with a global quench dual to AdS_33-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS_33 dual to a primary operator of dimension h in a large central charge expansion and explicitly compute both, the backreacted Ryu–Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by h/4h/4 in the large h expansion.

scholarly journals QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

2005 ◽  
Vol 17 (05) ◽  
pp. 577-612 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER ◽  
STEFAN HOLLANDS
Keyword(s):  
Field Theories ◽  
Positive Energy ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Conformal Field ◽  
Quantum Energy Inequalities ◽  
Stress Energy

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

scholarly journals AN EXPLICIT CONSTRUCTION OF WAKIMOTO REALIZATIONS OF CURRENT ALGEBRAS

1996 ◽  
Vol 11 (24) ◽  
pp. 1999-2011 ◽  
Author(s):  
JAN DE BOER ◽  
LÁSZLÓ FEHÉR
Keyword(s):  
Free Field ◽  
Explicit Construction ◽  
Hamiltonian Reduction ◽  
Energy Tensor ◽  
Parabolic Subalgebra ◽  
Standard Case ◽  
Normal Ordering ◽  
Free Field Realization ◽  
Stress Energy ◽  
Wakimoto Realization

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra [Formula: see text] can be associated with each parabolic subalgebra [Formula: see text] of the Lie algebra [Formula: see text], where in the standard case [Formula: see text] is the Cartan and [Formula: see text] is the Borel subalgebra. In this letter we obtain an explicit formula for the Wakimoto realization in the general case. Using Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket realization of the [Formula: see text]-valued current in terms of symplectic bosons belonging to [Formula: see text] and a current belonging to [Formula: see text]. We then quantize the formula by determining the correct normal ordering. We also show that the affine-Sugawara stress-energy tensor takes the expected quadratic form in the constituents.

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