Nonunitary higher derivative gravity classically equivalent to Einstein gravity and its Newtonian limit

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.

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

International Journal of Modern Physics D ◽

10.1142/s0218271813420157 ◽

2013 ◽

Vol 22 (12) ◽

pp. 1342015 ◽

Cited By ~ 10

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x00000197 ◽

2000 ◽

Vol 15 (03) ◽

pp. 413-428 ◽

Cited By ~ 115

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).

Holographic colour superconductors at finite coupling with NJL Interactions

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09931-x ◽

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.

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

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz084 ◽

2019 ◽

Vol 2019 (8) ◽

Cited By ~ 1

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.

Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit

Symmetry ◽

10.3390/sym12050752 ◽

2020 ◽

Vol 12 (5) ◽

pp. 752

Author(s):

Max Niedermaier

Keyword(s):

Scalar Field ◽

Parallel Transport ◽

Einstein Gravity ◽

Orthonormal Frame ◽

Newtonian Limit ◽

Index Structure ◽

Diffeomorphism Group ◽

Tensor Calculus ◽

Ehresmann Connection ◽

Spatio Temporal

A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport.

Background independence in string theory

International Journal of Modern Physics D ◽

10.1142/s0218271818470260 ◽

2018 ◽

Vol 27 (14) ◽

pp. 1847026

Author(s):

Olaf Hohm

Keyword(s):

Gauge Symmetry ◽

String Theory ◽

Degrees Of Freedom ◽

Einstein Gravity ◽

Background Independence ◽

Gauge Symmetries ◽

Higher Derivative ◽

Invariant Formulation

I discuss various aspects of background independence in the context of string theory, for which so far we have no manifestly background independent formulation. After reviewing the role of background independence in classical Einstein gravity, I discuss recent results implying that there is a conflict in string theory between manifest background independence and manifest duality invariance when higher-derivative corrections are included. The resolution of this conflict requires the introduction of new gauge degrees of freedom together with an enlarged gauge symmetry. This suggests more generally that a manifestly background independent and duality invariant formulation of string theory requires significantly enhanced gauge symmetries.

GRAVITATIONAL FIELD OF A STRAIGHT COSMIC STRING IN THE FRAMEWORK OF HIGHER-DERIVATIVE GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732308026145 ◽

2008 ◽

Vol 23 (24) ◽

pp. 1999-2009 ◽

Cited By ~ 2

Author(s):

ANTONIO ACCIOLY ◽

JOSÉ HELAYËL-NETO ◽

MATHEUS LOBO

Keyword(s):

Gravitational Field ◽

Cosmic String ◽

Short Range ◽

Gravitational Force ◽

Deflection Angle ◽

Einstein Gravity ◽

Nonrelativistic Limit ◽

Higher Derivative ◽

The Deflection Angle ◽

The Impact

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter.

Flow equation of quantum Einstein gravity in a higher-derivative truncation

Physical Review D ◽

10.1103/physrevd.66.025026 ◽

2002 ◽

Vol 66 (2) ◽

Cited By ~ 188

Author(s):

O. Lauscher ◽

M. Reuter

Keyword(s):

Einstein Gravity ◽

Flow Equation ◽

Higher Derivative

AdS/BCFT correspondence, holographic g-theorem and Gauss–Bonnet gravity

International Journal of Modern Physics A ◽

10.1142/s0217751x14501395 ◽

2014 ◽

Vol 29 (24) ◽

pp. 1450139 ◽

Cited By ~ 1

Author(s):

Bahman Najian

Keyword(s):

Central Charge ◽

Einstein Gravity ◽

Monotonicity Property ◽

Partition Functions ◽

Supporting Evidence ◽

Conformal Field Theories ◽

Conformal Field ◽

Trace Anomaly ◽

Higher Derivative ◽

Odd Dimensions

We investigate some aspects of holographic dual of boundary conformal field theories for higher derivative Gauss–Bonnet (GB) gravity. We explore the holographic g-theorem for GB gravity and introduce holographic g-functions in five and six dimensions. Focusing on the coefficients of the logarithmic terms in the partition functions of BCFTs holographically, and in the presence of higher derivative terms, in even dimensions we show that these are associated with corrected A-type trace anomaly. Building on this, in odd dimensions, we present supporting evidence for monotonicity property of boundary central charge in BCFT5 in Einstein gravity. However, in the GB gravity case, we find that the monotonicity behavior is violated. This invalidates the holographic g-theorem for the GB gravity.