We study the generalized minimal massive gravity (GMMG) in Compere, Song and Strominger boundary conditions employing a semi-product of a Virasoro and a $\hat{u}(1)$ Kac-Moody current algebras as the asymptotic symmetry algebra. We calculate the entropy of BTZ black holes via the degeneracy of states belonging to a Warped-CFT. We compute the linearized energy excitations by using the representations of the algebra $\hat{u}(1) \times SL(2,R)_R$ 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.
We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtai…
At a critical ``chiral'' coupling, topologically massive gravity with a negative cosmological constant exhibits several unusual features, including the emergence of a new logarithmic branch of solutions and a linearization instability for certain boundary conditions. I show that at this coupling, the linearized theory may be parametrized by a free scalar field at the Breitenlohner-Freedman bound, and use this description to investigate these features.
We compute the tree-level scattering amplitude between two covariantly conserved sources in generic Cosmological Topologically Massive Gravity augmented with a Fierz-Pauli term that has three massive degrees of freedom. We consider the Chiral Gravity limit in the anti-de Sitter space as well as the limit of Flat-Space Chiral Gravity. We show that Chiral Gravity cannot be unitarily deformed with a Fierz-Pauli mass. We calculate the non-relativistic potential energy between two point-like spinning sources. In addition to the expected mass-mass and spin-spin interactions, there are mass-spin inte…
To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter $μ$, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and…
Wolfgang Kummer was a pioneer of two-dimensional gravity and a strong advocate of the first order formulation in terms of Cartan variables. In the present work we apply Wolfgang Kummer's philosophy, the `Vienna School approach', to a specific three-dimensional model of gravity, cosmological topologically massive gravity at the chiral point. Exploiting a new Chern-Simons representation we perform a canonical analysis. The dimension of the physical phase space is two per point, and thus the theory exhibits a local physical degree of freedom, the topologically massive graviton.
We show that cosmological topologically massive gravity at the chiral point allows not only Brown-Henneaux boundary conditions as consistent boundary conditions, but slightly more general ones which encompass the logarithmic primary found in 0805.2610 as well as all its descendants.
We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the presence of a non-trivial trace and its logarithmic partner at the chiral point. The trace modes carry energy opposite in sign to the traceless modes. The logarithmic partner of the traceless mode carries negative energy indicating an instability at the chiral point. We make several comments on the…
We find the excitations and construct the conserved charges ( mass and angular momentum) of the recently found Minimal Massive Gravity (MMG) in 2+1 dimensions in asymptotically Anti-de Sitter (AdS) spacetimes. The field equation of the theory does not come from an action and hence lacks the required Bianchi Identity needed to define conserved charges. But the theory, which also provides a healthy extension of the Topologically Massive Gravity in the bulk and boundary of spacetime, does admit conserved charges for metric that are solutions. Our construction is based on background Killing vector…
We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of SU(2) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom…
We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L_0 and \bar{L}_0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than t…
Within mass perturbation theory, already the first order contribution to the chiral condensate of the massive Schwinger model is UV divergent. We discuss the problem of choosing a proper normalization and, by making use of some bosonization results, we are able to choose a normalization so that the resulting chiral condensate may be compared, e.g., with lattice data.
Università di Salerno（萨莱诺大学）；INFN Sezione di Napoli, Gruppo collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Czech Technical University in Prague（布拉格捷克技术大学）
Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two-dimensional conformal group and that included a fall-off of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp-waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely the chirality that has the milder behaviour at infinity. The other chirality blows up faster than AdS an…
We propose a new, chiral description for massive higher-spin particles in four spacetime dimensions, which facilitates the introduction of consistent interactions. As proof of concept, we formulate three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory or gravity. The theories are chiral and have simple Lagrangians, resulting in Feynman rules analogous to those of massive scalars. Starting from these Feynman rules, we derive tree-level scattering amplitudes with two higher-spin matter particles and any number of positive-helicity photons, gluons or …
We present a technique to construct, for $D_{m}$ unitary minimal models, the non-chiral fusion rules which determines the operator content of the operator product algebra. Using these rules we solve the bootstrap equations and therefore determine the structure constants of these models. Through this approach we emphasize the role played by some discrete symmetries in the classification of minimal models.
The Bargman-Wigner equations are generalized to include chiral symmetry based on the irreps of the Poincaré group, and the chirial Bargmann-Wigner equations are derived for spin-1 massive fields. By specifying the chiral basis, the chiral Bargmann-Wigner equations are reduced to the Proca-like equation, which is coupled by chirality to an auxiliary equation for spin-0 massive field. The coupling is a new phenomenon whose physical implications for the Higgs field and dark matter are discussed.
We show that a massive fermion theory, while not invariant under the conventional chiral transformation, is invariant under a $m$-deformed chiral transformation. These transformations and the associated conserved charges are nonlocal but reduce to the usual transformations and charges when $m=0$. The $m$-deformed charges commute with helicity and satisfy the conventional chiral algebra.
We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and locally scale covariant field equations are found by a first order variational formalism.
We reconsider the two-flavor version of the massive, chiral Gross-Neveu model in 1+1 dimensions. Its phase diagram as a function of baryon chemical potential, isospin chemical potential and temperature has previously been explored. We recapitulate the results, adding the missing tricritical curves. They can be determined exactly by extending the standard stability analysis, using fourth order almost degenerate perturbation theory. Results for three different bare masses are presented and discussed.
Although the chiral dotted spinor superfield should describe a Massive Superspin One Half multiplet, it has not been obvious how to derive this from an action. In this paper this is done by including a chiral undotted spinor superfield, finding the BRST transformations that govern both of these, and then finding the action as an invariant of the transformations. It turns out that both kinds of spinor superfields are needed. Moreover, the BRST transformations for the two kinds of chiral spinor superfields are generated from each other by a special involution that exchanges Grassmann odd (even) …
We consider the minimal chiral Schwinger model, by embedding the gauge noninvariant formulation into a gauge theory following the Batalin-Fradkin-Fradkina-Tyutin point of view. Within the BFFT procedure, the second class constraints are converted into strongly involutive first-class ones, leading to an extended gauge invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess-Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge noninvariant action.
We present an alternative to Topologically Massive Gravity (TMG) with the same "minimal" bulk properties; i.e. a single local degree of freedom that is realized as a massive graviton in linearization about an anti-de Sitter (AdS) vacuum. However, in contrast to TMG, the new "minimal massive gravity" has both a positive energy graviton and positive central charges for the asymptotic AdS-boundary conformal algebra.
A unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was first found in the light-cone gauge. We construct a covariant form of the corresponding field equations in all orders, thus completing the previous analysis of arXiv:2204.10285. This result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about counterterms, anomalies, etc.
We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.
We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of chiral gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a "chiral highest weight'' QNM which in turn satisfies a first order equation.
We study the complexity growth by using complexity = action (CA) proposal in Minimal Massive 3D Gravity(MMG) model which is proposed for resolving the bulk-boundary clash problem of Topologically Massive Gravity(TMG). We observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero.
We correct a sign in the first variation of the on-shell action of cosmological topologically massive gravity at the chiral point and present the three equations affected by that sign. While this does not change any of the main conclusions of arXiv:0805.2610, it modifies the finite part of the Brown-York stress tensor. Our corrected Brown-York stress tensor is still finite, conserved and traceless, but no longer coincides with that of global AdS_3. It agrees with results found in recent literature.
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.
Recently, an extension of the topologically massive gravity (TMG) in $2+1$ dimensions, dubbed as minimal massive gravity (MMG), was found which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three dimensional theories. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is …
We look at solutions of Minimal Massive Gravity (MMG), a generalisation of Topologically Massive Gravity (TMG) that improves upon its holographic properties. It is shown that generically (in MMG parameter space) all conformally flat solutions of vacuum MMG are locally isometric to one of the two (A)dS vacua of the theory. We then couple a scalar field, and find that domain wall solutions can only interpolate between these two vacua precisely when the bulk graviton is tachyonic. Finally, we find a non-BTZ AdS black hole solution satisfying Brown-Henneaux boundary conditions, which lies within t…
In this paper we construct mass, angular momentum and entropy of black hole solution of Generalized Minimal Massive Gravity (GMMG) in asymptotically Anti-de Sitter (AdS) spacetimes. The generalized minimal massive gravity theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. We apply our result for conserved charge $Q^μ (\barξ)$ to the rotating BTZ black hole solution of GMMG, and find energy, angular momentum and entropy. Then we show our results for these quantities are c…
We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of $ψ^{new}$ and $X$ are introduced for a candidate of propagating physical field at the chiral point. However, we show that ($ψ^{new},ψ^L$) form a dipole ghost pair of unphysical fields and $X$ is not a primary. This implies that there is no physically propagating degrees of freedom at the chiral point.
A recent paper [arXiv:0801.4566] claims that topologically massive gravity contains only chiral boundary excitations at a particular value of the Chern-Simons coupling. On the other hand, propagating bulk degrees of freedom were found even at the chiral point in [arXiv:0803.3998]. The two references use very different methods, making comparison of their respective claims difficult. In this letter, we use the method of [arXiv:0801.4566] to construct a tower of propagating bulk states satisfying standard AdS boundary conditions. Our states have finite norm, with sign opposite to that of right-mo…
The graviton 1-loop partition function in Euclidean topologically massive gravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.
We construct a Weyl-invariant extension of topologically massive gravity which, remarkably, turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters, therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low ener…
We study the system of a massive fermion field confined between two parallel plates, where the properties of both plates are discussed under chiral MIT boundary conditions. We investigate the effects of the chiral angle on the Casimir energy for a massive fermion field with the general momentum. We find that the Casimir energy as a function of the chiral angle is generally symmetric, and the attractive Casimir force in the chiral case is stronger than that in the nonchiral case. In addition, we investigate the approximate Casimir energy for light and heavy mass cases. The behavior of the discr…
The "Minimal Massive Gravity" (MMG) model of massive gravity in three spacetime dimensions (which has the same anti-de Sitter (AdS) bulk properties as "Topologically Massive Gravity" but improved boundary properties) is coupled to matter. Consistency requires a particular matter source tensor, which is quadratic in the stress tensor. The consequences are explored for an ideal fluid in the context of asymptotically de-Sitter (dS) cosmological solutions, which bounce smoothly from contraction to expansion. Various vacuum solutions are also found, including warped-(A)dS, and (for special values o…
We evaluate Polyakov loops and string tension in two-dimensional QED with both massless and massive $N$-flavor fermions at zero and finite temperature. External charges, or external electric fields, induce phases in fermion masses and shift the value of the vacuum angle parameter $θ$, which in turn alters the chiral condensate. In particular, in the presence of two sources of opposite charges, $q$ and $-q$, the shift in $θ$ is $2π(q/e)$ independent of $N$. The string tension has a cusp singularity at $θ=\pmπ$ for $N\ge 2$ and is proportional to $m^{2N/(N+1)}$ at $T=0$.
We construct Kundt solutions of Minimal Massive Gravity theory and show that, similar to Topologically Massive Gravity (TMG), most of them are constant scalar invariant (CSI) spacetimes, that correspond to deformations of round and warped (A)dS. We also find an explicit non-CSI Kundt solution at the merger point. Finally, we give their algebraic classification with respect to the traceless Ricci tensor (Segre classification) and show that their Segre-types match with the types of their counterparts in TMG.
We study the algebra of SU(n)-currents in the many-flavor chiral Gross-Neveu model. The general structure of the current-current OPE leading to non-local quantum conserved charges is reviewed. We calculate the OPE in the one-flavor and the many-flavor models perturbatively and use renormalization group invariance to prove that our results are not altered by higher-order corrections. We conclude that in these models the non-local quantum charge exists which is the first step towards the proof of the absence of particle production and factorization.
The phase diagram of the massive chiral Gross-Neveu model (the 1+1-dimensional Nambu-Jona-Lasinio model at large N) is investigated in the vicinity of the tricritical point. Using the derivative expansion, the grand canonical potential is cast into the form of a Ginzburg-Landau effective action. Minimization of this action by variational and numerical methods reveals both 1st and 2nd order phase transitions to a chiral crystal phase, separated by a tricritical line. These findings are contrasted to the massive Gross-Neveu model with discrete chiral symmetry where only 2nd order transitions hav…
We argue that the self/anti-self charge conjugate states of the (1/2,0)\oplus (0,1/2) representation possess the axial charge. Furthermore, we analyze the recent claims of the \sim σ\cdot [A \times A^*] interaction terms for `fermions'. Finally, we briefly discuss the problem in the (1,0)\oplus (0,1) representation.
In this note we investigate the generalized massive gravity in asymptotically $AdS_3$ spacetime by combining the two mass terms of topological massive gravity and new massive gravity theory. We study the linearized excitations around the $AdS_3$ background and find that at a specific value of a certain combination of the two mass parameters (chiral line), one of the massive graviton solutions becomes the left moving massless mode. It is shown that the theory is chiral at this line under Brown-Henneaux boundary condition. Because of this degeneration of the gravitons the new log solution which …
The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature and compared with the one of th…
A variant for the superspin one-half massive superparticle in $ 4D $, $ \mathcal{N}=1 $, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the supermultiplet are those of the lowest mass dimensions possible: scalar, Dirac and vector fields. Besides the supersymmetric chiral condition, the Dirac superfields are not further constrained, allowing a very straightforward implementation of the path-integral method. The corresponding superpropagators are presented. In addition, an interaction super Yukawa poten…
In this paper, we study the spin-3 topological massive gravity(TMG), paying special attention to its properties at the chiral point. We propose an action describing the high spin fields coupled to TMG. We discuss the spin-3 fluctuations around the AdS$_3$ vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin…
We present a covariant nonlinear completion of the Fierz-Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin--connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Eins…
There exists a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a Free Differential Algebra up to NLO, i.e. at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space exte…
In this paper we systematically construct simply transitive homogeneous spacetime solutions of the three-dimensional Minimal Massive Gravity (MMG) model. In addition to those that have analogs in Topologically Massive Gravity, such as warped AdS and pp-waves, there are several solutions genuine to MMG. Among them, there is a stationary Lifshitz metric with the dynamical exponent z=-1 and an anisotropic Lifshitz solution where all coordinates scale differently. Moreover, we identify a homogeneous Kundt type solution at the chiral point of the theory. We also show that in a particular limit of t…
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering four N=1 chiral superfields with global Lorentz symmetry. When the scalar components of the chiral multiplets z^A acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. The global Lorentz index A becomes identified with the space-time Lorentz index making the scalar fields z^A vectors and the chiral…
We show that in certain limits the (1+1)-dimensional massive Thirring model at finite temperature $T$ is equivalent to a one-dimensional Coulomb gas of charged particles at the same $T$. This equivalence is then used to explore the phase structure of the massive Thirring model. For strong coupling and $T>>m$ (the fermion mass) the system is shown to behave as a free gas of "molecules" (charge pairs in the Coulomb gas terminology) made of pairs of chiral condensates. This binding of chiral condensates is responsible for the restoration of chiral symmetry as $T\to\infty$. In addition, when a fer…
We formulate a complete path integral bosonization procedure for any fermionic theory in two dimensions. The method works equally well for massive and massless fermions, and is a generalization of an approach suggested earlier by Andrianov. The classical action of the bosons in the bosonized theory is identified with -i times the logarithm of the Jacobian of a local chiral transformation, with the boson fields as transformation parameters. Three examples, the Schwinger model, the massive Thirring model and massive non-Abelian bosonization, are worked out.
Using Random Matrix Theory we set out to compute the microscopic correlators of the Euclidean Dirac operator in four dimensions. In particular we consider: the chiral Orthogonal Ensemble (chOE), corresponding to a Yang-Mills theory with two colors and fermions in the fundamental representation, and the chiral Symplectic Ensemble (chSE), corresponding to any number of colors and fermions in the adjoint representation. In both cases we deal with an arbitrary number of massive fermions. We use a recent method proposed by H. Widom for deriving closed formulas for the scalar kernels from which all …
(Talk presented at the 1992 ICTP summer workshop in high energy physics and cosmology) The BRST cohomology ring for $(p,q)$ models coupled to gravity is discussed. In addition to the generators of the ghost number zero ring, the existence of a generator of ghost number $-1$ and its inverse is proven and used to construct the entire ring. Some comments are made regarding the algebra of the vector fields on the ring and the supersymmetric extension.
