Minimal Massive Gravity Research Articles

Minimal massive supergravity and new theories of massive gravity

We present an action for minimal massive gravity (MMG) in three dimensions in terms of a dreibein and an independent spin connection. Furthermore, the construction provides an action principle for an infinite family of so-called third-way consistent generalizations of the three-dimensional Einstein field equations, including exotic massive gravity and new higher-order generalizations. It allows us to systematically construct the matter couplings for these models, including the couplings to fermions, depending on the spin connection. In particular, we construct different supersymmetric extensions of MMG, and derive their second order fermionic field equations. This establishes a new class of three-dimensional supergravity theories and we discuss their limit to topological massive supergravity. Finally, we identify the landscape of (anti–)de Sitter vacua of the supersymmetric models. We analyze the spectrum and the unitarity properties of these vacua. We recover the known AdS vacua of MMG which are bulk and boundary unitary. Published by the American Physical Society 2024

Minimal Massive Supergravity.

Minimal massive gravity in three dimensions propagates a single massive spin-2 mode around an anti-de Sitter vacuum. It is distinguished by allowing for vacua with positive central charges of the asymptotic conformal algebra and a bulk graviton of positive energy. We present a new action for the model (and its higher order extensions) in terms of a dreibein and an independent spin connection. From this, we construct its supersymmetric extension. Surprisingly, all vacua complying with bulk and boundary unitarity appear to break supersymmetry spontaneously. In contrast, all supersymmetric vacua have a negative central charge whenever the bulk graviton has positive energy.

Holographic entanglement entropy in $$T{\bar{T}}$$-deformed CFTs

In this paper, we study the holographic entanglement entropy computation of the ultraviolet, integrable deformation of the $$2-$$ dimensional conformal field theory ( $$T{\bar{T}}$$ -deformed conformal field theory) that would be dual to some massive deformations of 3D gravity in asymptotically $$AdS_{3}$$ spacetimes. We compute the correction due to the deformation up to the leading order of the deformation parameter in higher curvature 3D gravities such as new massive gravity, general minimal massive gravity, and exotic general massive gravity. We also use the evaluation of the symplectic potential to obtain the entanglement entropy for deformed theories. In each case, we find agreement between the results.

Hairy black holes in general minimal massive gravity

In this work, we investigate the near horizon and asymptotic symmetries of static and rotating hairy-AdS black hole in the framework of general minimal massive gravity. We obtain energy, angular momentum and entropy of the solutions. Then we show that our results for these quantities are consistent with the first law of black hole thermodynamics. By considering the near horizon geometry of black hole, we find near horizon conserved charges and their algebra. By writing the algebra of conserved charges in terms of Fourier modes we have obtained the conserved charges in terms of zero modes.

A note on the pp-wave solution of minimal massive 3D gravity coupled with Maxwell–Chern–Simons theory

In this work, we examine a family of pp-wave solutions of minimal massive 3D gravity minimally coupled with the Maxwell–Chern–Simons theory. An elaborate investigation of the field equations shows that the theory admits pp-wave solutions provided that there exist an anti-self duality relation between the electric and the magnetic components of the Maxwell two-form field. By employing Noether–Wald formalism, we also construct Noether charges of the theory within exterior algebra formalism.

A note on the third way consistent deformation of Yang-Mills theory

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the equation, realizing a spin-1 analogue of ‘minimal massive gravity’, which has been dubbed ‘third way consistent’. In this note, we show that after dualization of the three-dimensional gauge fields, the model possesses a natural action as a Chern-Simons coupled gauged sigma model. In this dual formulation, coupling to matter and to gravity becomes straightforward. As a direct application, we derive the coupling of the model to N=1 supergravity.

Canonical description of exotic general massive gravity

Exotic General Massive Gravity is the next-to-simplest gravitational theory fulfilling the so-called third-way consistency, the simplest being Minimal Massive Gravity. We investigate the canonical structure of the first-order formulation of Exotic General Massive Gravity. By using the Dirac Hamiltonian formalism, we systematically discover the complete set of physical constraints, including primary, secondary, and tertiary ones, and explicitly compute the Poisson bracket algebra between them. In particular, we demonstrate that the consistency condition for the tertiary constraints provides explicit expressions which can be solved algebraically for the auxiliary fields f and h in terms of the dreibein e. In this configuration, to confirm that the theory is ghost-free, the whole set of constraints is classified into first and second-class ones showing the existence of only two physical degrees of freedom corresponding to one massive graviton. Furthermore, we identify the transformation laws for all of the dynamical variables corresponding essentially to gauge symmetries, generated by the first-class constraints. Finally, by taking into account all the second-class constraints, we explicitly compute the Dirac matrix together with the Dirac’s brackets.

Holographic entanglement negativity in flat space generalized minimal massive gravity

In this paper, we study the application of holographic entanglement negativity proposal for bipartite states in the 2D Galilean conformal field theory [Formula: see text] dual to bulk asymptotically flat space–times in the context of generalized minimal massive gravity (GMMG) model. [Formula: see text] is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the entanglement negativity are obtained in the bipartite configurations of the system in the boundary.

Conserved charges of GMMG in arbitrary backgrounds

We extend the Abbott–Deser–Tekin (ADT) method to the computation of the global charges associated with Killing vectors of the background for solutions of general minimal massive gravity (GMMG) linearized about an arbitrary background. Then, we implement our result in various solutions to evaluate the mass and angular momentum with arbitrary asymptotics.

Matter coupling in minimal massive 3D gravity and spinor-matter interactions in exterior algebra formalism

In this work, by employing the exterior algebra formalism, we study the matter coupling in minimal massive 3D gravity (MMG) by first considering that the matter Lagrangian is connection-independent and then considering that the matter coupling is connection-dependent. The matter coupling in MMG has been previously investigated in the work Arvanitakis et al (2014 Class. Quantum Grav. 31 235012) in tensorial notation where the matter Lagrangian is considered to be connection-independent. In the first part of the present paper, we revisit the connection-independent matter coupling by using the language of differential forms. We derive the MMG field equation and construct the related source two-form. We also obtain the consistency relation within this formalism. Next, we examine the case where the matter Lagrangian is connection-dependent. In particular, we concentrate on the spinor-matter coupling and obtain the MMG field equation by explicitly constructing the source term. We also get the consistency relation that the source term should satisfy in order that spinor-matter coupled MMG equation be consistent.

Holographic entanglement entropy and modular Hamiltonian in warped CFT in the framework of GMMG model

We study some aspects of a class of non-AdS holography where the 3D bulk gravity is given by generalized minimal massive gravity (GMMG). We consider the spacelike warped AdS_3 (WAdS_3) black hole solution of this model where the 2d dual boundary theory is the warped conformal field theory (WFCT). The charge algebra of the isometries in the bulk and the charge algebra of the vacuum symmetries at the boundary are compatible and this is an evidence for the duality conjecture. Further evidence for this duality is the equality of entanglement entropy and modular Hamiltonian on both sides of the duality. So we consider the modular Hamiltonian for the single interval at the boundary in associated to the modular flow generators of the vacuum. We calculate the gravitational charge in associated to the asymptotic Killing vectors that preserve the metric boundary conditions. Assuming the first law of the entanglement entropy to be true, we introduce the matching conditions between the variables in two side of the duality and we find equality of the modular Hamiltonian variations and the gravitational charge variations in two sides of the duality. According to the results of the present paper we can say with more sure that the dual theory of the warped AdS3 black hole solution of GMMG is a Warped CFT.

Flat limit chiral gravity in GMMG and EGMG

In this work we extend the holographic correspondence between flat space limit of chiral topological massive gravity and a specific unitary field theory to flat space limit of chiral general minimal massive gravity and chiral exotic general massive gravity. To check the conjecture, we compare the entropy and partition function of flat limit of BTZ black hole from viewpoint of both sides.

New chiral generalized minimal massive gravity

We study the generalized minimal massive gravity (GMMG) in Compere, Song, and Strominger boundary conditions employing a semiproduct of Virasoro and $\stackrel{^}{u}(1)$ Kac-Moody current algebras as the asymptotic symmetry algebra. We calculate the entropy of Ba\~nados-Teitelboim-Zanelli black holes via the degeneracy of states belonging to a Warped conformal field theory. We compute the linearized energy excitations by using the representations of the algebra $\stackrel{^}{u}(1)\ifmmode\times\else\texttimes\fi{}SL(2,R{)}_{R}$ and show that energies of excitations are non-negative at (two) chiral points in the parameter space. At these special points, the charge algebra is described by either Virasoro algebra or Kac-Moody algebra. We also consider some special limits of the GMMG theory which correspond to $2+1$-dimensional massive gravity theories such as new massive and minimal massive gravity theories.

Holographic entanglement entropy in flat limit of the generalized minimal massive gravity model

Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in asymptotically AdS_3 background, and have shown that the theory is free of negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned “bulk-boundary unitarity clash”. Here instead of AdS_3 space we consider asymptotically flat space, and study this model in the flat limit. The dual field theory of GMMG in the flat limit is a BMS_3 invariant field theory, dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro algebra. In fact here we present an evidence for this claim. Entanglement entropy of GMMG is calculated in the background in the flat null infinity. Our evidence for mentioned claim is the result for entanglement entropy in filed theory side and in the bulk (in the gravity side). At first using Cardy formula and Rindler transformation, we calculate entanglement entropy of BMSFT in three different cases. Zero temperature on the plane and on the cylinder, and non-zero temperature case. Then we obtain the entanglement entropy in the bulk. Our results in gravity side are exactly in agreement with field theory calculations.

Phase transition between flat space cosmology and hot flat spacetimes in GMMG and EGMG models

Flat space cosmology (FSC) spacetimes are exact solutions of 3D gravity theories. In this work, we study phase transition between FSC spacetimes and hot flat spacetimes (HFS) in general minimal massive gravity and exotic general massive gravity. We show that similar to topological massive gravity the tunneling occurs between two spacetimes by comparing their free energies. We also obtain the corrections to the Bekenstein−Hawking entropy, and its effect on the phase transition is studied.

Spontaneously broken 3d Hietarinta/Maxwell Chern\u2013Simons theory and minimal massive gravity

We show that minimal massive 3d gravity (MMG) of (Bergshoeff et al. in Class Quantum Grav 31:145008, 2014), as well as the topological massive gravity, are particular cases of a more general ‘minimal massive gravity’ theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern–Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.

On asymptotic charges in 3D gravity

A variant of the ADT method for the determination of gravitational charges as integrals at infinity is applied to ‘Chern–Simons-like’ theories of 3D gravity, and the result is used to find the mass and angular momentum of the BTZ black hole considered as a solution of a variety of massive 3D gravity field equations. The results agree with many obtained previously by other methods, including our own results for ‘Minimal Massive Gravity’, but they disagree with others, including recently reported results for ‘Exotic Massive Gravity’. We also find the central charges of the asymptotic conformal symmetry algebra for the generic 3D gravity model with AdS vacuum and discuss implications for black hole thermodynamics.

Weyl covariant theories of gravity in 3-dimensional Riemann–Cartan–Weyl space-times

We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann–Cartan–Weyl space-times in arbitrary dimensions. We illustrate the procedure of Weyl gauging for three examples: general relativity, topologically massive gravity and minimal massive gravity theories in three dimensions. Afterwards, we demonstrate the consistency of scale covariant generalisation by showing that the scale covariant theories contain the original theories in their vacuum configuration for their Weyl sector.

Metric formulation of the simple theory of 3d massive gravity

We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal Lorentz gauge symmetry is broken. The absence of Lorentz invariance, which in this model is the mechanism underlying the propagation of a massive graviton, does however prevent from writing a purely metric non-linear action for the theory. Nonetheless, in this letter, we explain how to disentangle, at the non-linear level, the metric and non-metric degrees of freedom in the equations of motion. Focusing on the metric part, we show that it satisfies modified Einstein equations with higher derivative terms. As a particular case, these equations reproduce a well-studied model known as minimal massive gravity. In the general case, we obtain new metric field equations for massive gravity in three dimensions starting from the simple first order action. These field equations are consistent through a mechanism known as "third way consistency", which our theory therefore provides a new example of.

Circularly symmetric solutions of minimal massive gravity at its merger point

I find all the static circularly symmetric solutions of minimal massive 3D gravity at its merger point, construct stationary versions of these and discuss some of their geometric and physical properties. It turns out that apart from a static hairy black hole, there is also a static gravitational soliton, that has been overlooked in the literature.