scholarly journals Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1408
Author(s):  
Taichiro Kugo
Keyword(s):  
Field Equation ◽  
Linear Combination ◽  
Source Term ◽  
Equations Of Motion ◽  
High Order Derivative ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Brs Symmetry ◽  
Noether Current ◽  
Global Translation

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s IOSp(8|8) choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term.

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

scholarly journals Holographic entanglement entropy, field redefinition invariance, and higher derivative gravity theories

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
M. R. Mohammadi Mozaffar ◽  
A. Mollabashi ◽  
M. M. Sheikh-Jabbari ◽  
M. H. Vahidinia
Keyword(s):  
Entanglement Entropy ◽  
Holographic Entanglement Entropy ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Field Redefinition

scholarly journals AdS backgrounds and induced gravity

2019 ◽  
Vol 34 (38) ◽  
pp. 2050057
Author(s):  
Hai Lin ◽  
Gaurav Narain
Keyword(s):  
Scalar Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Equation Of Motion ◽  
Induced Gravity ◽  
Expectation Value ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Fluctuation Fields ◽  
Ads Geometry

In this paper, we look for AdS solutions to generalized gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein–Hilbert gravity is induced when the scalar acquires a nonzero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

Renormalization and unitarity in higher derivative and nonlocal gravity theories

2015 ◽  
Vol 30 (03n04) ◽  
pp. 1540005 ◽  
Author(s):  
E. T. Tomboulis
Keyword(s):  
Quantum Gravity ◽  
Fixed Points ◽  
Fourth Order ◽  
Entire Functions ◽  
Gravitational Action ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Fixed Order ◽  
Gravity Theories

We review and discuss higher derivative and nonlocal theories of quantum gravity focusing on their UV and unitarity properties. We first consider the general fourth-order gravitational action, then actions containing derivatives up to any given fixed order, and discuss their UV divergences, fixed points and concomitant unitarity issues. This leads to a more general discussion of "asymptotic safety" and unitarity, which motivates the introduction of nonlocal theories containing derivatives to all orders arising from the expansion of entire functions. For such theories good UV behavior is visible at any finite truncation, but unitarity emerges only when derivatives to all orders are included.

scholarly journals A NOTE ON SUPERSYMMETRIC WZW TERM IN FOUR DIMENSIONS

2000 ◽  
Vol 15 (38n39) ◽  
pp. 2327-2333 ◽  
Author(s):  
MUNETO NITTA
Keyword(s):  
Equations Of Motion ◽  
Total Derivative ◽  
Four Dimensions ◽  
Anomalous Term ◽  
Higher Derivative ◽  
Derivative Term ◽  
Chiral Superfields

We reconsider the supersymmetric Wess–Zumino–Witten (SWZW) term in four dimensions. It has been known that the manifestly supersymmetric form of the SWZW term includes derivative terms on auxiliary fields, the highest components of chiral superfields, and then we cannot eliminate them by their equations of motion. We discuss a possibility for the elimination of such derivative terms by adding total derivative terms. Although most of the derivative terms can be eliminated in this way, we find that all the derivative terms can be canceled, if and only if an anomalous term in SWZW term vanishes. As a by-product, we find the first example of a higher derivative term free from such problem.

scholarly journals Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Sera Cremonini ◽  
Callum R.T. Jones ◽  
James T. Liu ◽  
Brian McPeak
Keyword(s):  
Black Holes ◽  
Equations Of Motion ◽  
Casimir Energy ◽  
Thermodynamic Quantities ◽  
Leading Order ◽  
De Sitter ◽  
Higher Derivative ◽  
Positive Meaning ◽  
Universal Relationship ◽  
Weak Gravity

Abstract We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c − a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.

scholarly journals Electromagnetic quasitopological gravities

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Pablo A. Cano ◽  
Ángel Murcia
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Maxwell Theory ◽  
Fully Integrated ◽  
Higher Derivative ◽  
Metric Function ◽  
Minimal Mass ◽  
Extremal Black Holes

Abstract We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function f (r) = −gtt = 1/grr. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for f (r). Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

scholarly journals Galileon string measure and other modified measure extended objects

2017 ◽  
Vol 32 (38) ◽  
pp. 1750211 ◽  
Author(s):  
T. O. Vulfs ◽  
E. I. Guendelman
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Equations Of Motion ◽  
String Tension ◽  
Gauge Transformations ◽  
Higher Derivative ◽  
Dynamical Degree ◽  
Integration Measure ◽  
Definition Of ◽  
Galileon Field

We show that it is possible to formulate string theory as a “Galileon string theory”. The Galileon field [Formula: see text] enters in the definition of the integration measure in the action. Following the methods of the modified measure string theory, we find that the final equations are again those of the sigma-model. Moreover, the string tension appears again as an additional dynamical degree of freedom. At the same time, the theory satisfies all requirements of the Galileon higher derivative theory at the action level while the equations of motion are still of the second-order. A Galileon symmetry is displayed explicitly in the conformal string worldsheet frame. Also, we define the Galileon gauge transformations. Generalizations to branes with other modified measures are discussed.

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