SOLVING THE RIDDLE OF THE INCOMPATIBILITY BETWEEN RENORMALIZABILITY AND UNITARITY IN N-DIMENSIONAL EINSTEIN GRAVITY ENLARGED BY CURVATURE-SQUARED TERMS

2013 ◽  
Vol 22 (12) ◽  
pp. 1342015 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
JOSÉ HELAYËL-NETO ◽  
ESLLEY SCATENA ◽  
RODRIGO TURCATI
Keyword(s):  
Gravitational Potential ◽  
Physical Theory ◽  
Einstein Gravity ◽  
Simple Solution ◽  
Tree Level ◽  
Main Argument ◽  
Higher Derivative

One of the puzzling aspects of N-dimensional Einstein Gravity (NDEG) augmented by curvature-squared terms is why renormalizability and unitarity, two of the most important properties of any physical theory, cannot be reconciled in its framework. Actually, the reason why these properties are mutually incompatible within the context of generic higher-derivative models, not necessarily related to gravity, is one of the unsolved mysteries of physics. Here, a simple solution to the NDEG riddle, based on the analysis of the interparticle gravitational potential, is presented. The main argument used to support our discussion is that tree-level unitarity and the existence of a singularity in the potential are intertwined.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

scholarly journals Black hole evaporation in Hořava–Lifshitz gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Hao Xu ◽  
Yen Chin Ong
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Lorentz Invariance ◽  
Detailed Balance ◽  
Einstein Gravity ◽  
Zero Temperature ◽  
Black Hole Mass ◽  
Black Hole Evaporation ◽  
Higher Derivative ◽  
Temperature State

Abstract Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter $$0\leqslant \epsilon ^2\leqslant 1$$0⩽ϵ2⩽1. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $$d=4,5$$d=4,5 behave differently from $$d\geqslant 6$$d⩾6. For the case of $$\epsilon =0$$ϵ=0, in $$d=4,5$$d=4,5, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As $$d\geqslant 6$$d⩾6, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of $$\ell ^{d-1}$$ℓd-1, similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to $$\epsilon ^2=1$$ϵ2=1), though for the latter this holds for all $$d\geqslant 4$$d⩾4. The case of $$0<\epsilon ^2<1$$0<ϵ2<1 is also qualitatively similar with $$\epsilon =0$$ϵ=0.

scholarly journals ON THE CONFORMAL ANOMALY FROM HIGHER DERIVATIVE GRAVITY IN AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (03) ◽  
pp. 413-428 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Einstein Gravity ◽  
Low Energy ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Higher Derivative

We follow Witten's proposal1 in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above (d + 1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L =aR2 + bRμνRμν + Λ (even when a=0 or b=0) is five-dimensional bulk theory for [Formula: see text] super-Yang–Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of [Formula: see text] supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).

scholarly journals Classical and tree-level approaches to gravitational deflection in higher-derivative gravity

2015 ◽  
Vol 91 (12) ◽  
Author(s):  
Antonio Accioly ◽  
José Helayël-Neto ◽  
Breno Giacchini ◽  
Wallace Herdy
Keyword(s):  
Tree Level ◽  
Higher Derivative ◽  
Gravitational Deflection

scholarly journals Holographic colour superconductors at finite coupling with NJL Interactions

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Kazem Bitaghsir Fadafan ◽  
Jesús Cruz Rojas
Keyword(s):  
Equation Of State ◽  
Cooper Pair ◽  
Chemical Potential ◽  
Coupling Parameter ◽  
Einstein Gravity ◽  
Superconducting Phase ◽  
Holographic Model ◽  
Higher Derivative ◽  
Holographic Qcd ◽  
Holographic Description

AbstractWe study a bottom-up holographic description of the QCD colour superconducting phase in the presence of higher derivative corrections. We expand this holographic model in the context of Gauss–Bonnet (GB) gravity. The Cooper pair condensate has been investigated in the deconfinement phase for different values of the GB coupling parameter $$\lambda _{G B}$$ λ GB , we observe a change in the value of the critical chemical potential $$\mu _c$$ μ c in comparison to Einstein gravity. We find that $$\mu _c$$ μ c grows as $$\lambda _{G B}$$ λ GB increases. We add four fermion interactions and show that in the presence of these corrections the main interesting features of the model are still present and that the intrinsic attractive interaction can not be switched off. This study suggests to find GB corrections to equation of state of holographic QCD matter.

scholarly journals $S$ -matrix unitarity and renormalizability in higher-derivative theories

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Yugo Abe ◽  
Takeo Inami ◽  
Keisuke Izumi ◽  
Tomotaka Kitamura ◽  
Toshifumi Noumi
Keyword(s):  
Gauge Theories ◽  
Einstein Gravity ◽  
Field Theories ◽  
Kinetic Term ◽  
Negative Norm ◽  
Unitarity Bound ◽  
Higher Derivative ◽  
S Matrix ◽  
Scalar Field Models ◽  
Consistency Requirement

Abstract We investigate the relation between $S$-matrix unitarity ($SS^\dagger=1$) and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the $S$-matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the $S$-matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for $S$-matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.

Sign in / Sign up

Export Citation Format

Share Document