Chiral Gravity Research Articles

Boundary stress tensor and asymptoticallyAdS3non-Einstein spaces at the chiral point

Chiral gravity admits asymptotically ${\mathrm{AdS}}_{3}$ solutions that are not locally equivalent to ${\mathrm{AdS}}_{3}$; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally ${\mathrm{AdS}}_{3}$ solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally ${\mathrm{AdS}}_{3}$ solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally ${\mathrm{AdS}}_{3}$ solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote ${\mathrm{AdS}}_{3}$ space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

Addition of torsion to chiral gravity

Three-dimensional gravity in Anti-de Sitter space is considered, including torsion. The derivation of the central charges of the algebra that generates the asymptotic isometry group of the theory is reviewed, and a special point of the theory, at which one of the central charges vanishes, is compared with the chiral point of topologically massive gravity. This special point corresponds to a singular point in Chern-Simons theory, where one of the two coupling constants of the SL(2,R) actions vanishes. A prescription to approach this point in the space of parameters is discussed, and the canonical structure of the theory is analyzed.

Higgsing M2 to D2 with gravity: $ \mathcal{N} = 6 $ chiral supergravity from topologically gauged ABJM theory

We present the higgsing of three-dimensional N=6 superconformal ABJM type theories coupled to conformal supergravity, so called topologically gauged ABJM theory, thus providing a gravitational extension of previous work on the relation between N M2 and N D2-branes. The resulting N=6 supergravity theory appears at a chiral point similar to that of three-dimensional chiral gravity introduced recently by Li, Song and Strominger, but with the opposite sign for the Ricci scalar term in the lagrangian. We identify the supersymmetry in the broken phase as a particular linear combination of the supersymmetry and special conformal supersymmetry in the original topologically gauged ABJM theory. We also discuss the higgsing procedure in detail paying special attention to the role played by the U(1) factors in the original ABJM model and the U(1) introduced in the topological gauging.

THE MODIFIED BARGMANN-WIGNER FORMALISM FOR HIGHER SPIN FIELDS AND RELATIVISTIC QUANTUM MECHANICS

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons and fermions. Connections with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2 S +1) theory are found. Next, we proceed to derive the equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of results we generalize the standard procedure and we obtain the spin-2 relativistic equations, which are consistent with the Einstein-Hilbert equation. We introduce the dual analogues of the Riemann tensor and we derive corresponding dynamical equations in the Minkowski space. Connections with the Marques-Spehler chiral gravity theory are discussed. The importance of the 4-vector field (and its gauge part) is pointed out. The spin-3/2 case is briefly discussed too.

Non-Einstein geometries in chiral gravity

We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on non-Einstein metrics. A class of such solutions admits curvature singularities in the interior which are reflected as singularities or infinite bulk energy of the corresponding linear solutions. A non-linear solution is found exactly. The back-reaction induces a repulsion of geodesics and a shielding of the singularity by an event horizon but also introduces closed timelike curves.

Testing parity-violating mechanisms with cosmic microwave background experiments

Chiral gravity and cosmological birefringence both provide physical mechanisms to produce parity-violating $TB$ and $EB$ correlations in the cosmic microwave background (CMB) temperature/polarization. Here, we study how well these two mechanisms can be distinguished if nonzero $TB/EB$ correlations are found. To do so, we evaluate the correlation matrix, including new $TB\mathrm{\text{\ensuremath{-}}}EB$ covariances. We find that the effects of these two mechanisms on the CMB are highly orthogonal, and can thus be distinguished fairly well in the case of a high-signal-to-noise detection of $TB/EB$ correlations. Appendix B evaluates the relative sensitivities of the $BB$, $TB$, and $EB$ signals for detecting a chiral gravitational-wave background.

Chiral gravity, log gravity, and extremal CFT

We show that the linearization of all exact solutions of classical chiral gravity around the ${\mathrm{AdS}}_{3}$ vacuum have positive energy. Nonchiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity---the theory with logarithmically relaxed boundary conditions---has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic conformal field theories (CFT). Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We formally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.

No chiral truncation of quantum log gravity?

At the classical level, chiral gravity may be constructed as a consistent truncation of a larger theory called log gravity by requiring that left-moving charges vanish. In turn, log gravity is the limit of topologically massive gravity (TMG) at a special value of the coupling (the chiral point). We study the situation at the level of linearized quantum fields, focussing on a unitary quantization. While the TMG Hilbert space is continuous at the chiral point, the left-moving Virasoro generators become ill-defined and cannot be used to define a chiral truncation. In a sense, the left-moving asymptotic symmetries are spontaneously broken at the chiral point. In contrast, in a non-unitary quantization of TMG, both the Hilbert space and charges are continuous at the chiral point and define a unitary theory of chiral gravity at the linearized level.

Stability of warpedAdS3vacua of topologically massive gravity

AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point \mu l=1. We study the possibility that the warped vacua of TMG, which exist for all values of \mu, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range \mu l > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons.

Chiral supergravity

We study the linearized approximation of N=1 topologically massive supergravity around AdS3. Linearized gravitino fields are explicitly constructed. For appropriate boundary conditions, the conserved charges demonstrate chiral behavior, so that chiral gravity can be consistently extended to chiral supergravity.

Standard model and gravity from spinors

It is shown how the Lorentz and standard-model gauge groups can be unified by using algebraic spinors of the standard four-dimensional Clifford algebra, in left–right symmetric fashion. This defines a framework of unification with gravity and generates exactly a standard-model family of fermions, while a Pati–Salam unification group emerges, at the Planck scale, where (chiral) gravity decouples. We show that this low-energy broken phase emerges from the VEV of extended vierbein fields, which at this stage are assumed to be dynamically generated from a theory in the fully symmetric phase valid beyond the Planck scale (and whose consistency and dynamics is thus yet to be assessed) providing thus a geometrical and group-theoretical framework for the unification and breaking. At low energy, on the other hand, it is intriguing to find, as a remnant of this unification, new isospin-triplet spin-two particles that may naturally lie at the weak scale, providing a striking signal at the LHC.

Logarithmic conformal field theory approach to topologically massive gravity

We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of ψnew and X are introduced for a candidate of propagating physical field at the chiral point. However, we show that (ψnew,ψL) 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.

Instability in cosmological topologically massive gravity at the chiral point

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 the ones by Brown and Henneaux, its fall-off behavior is compatible with spacetime being asymptotically AdS_3. We employ holographic renormalization to show that the variational principle is well-defined. The corresponding Brown-York stress tensor is finite, traceless and conserved. Finally we address possibilities to eliminate the instability and prospects for chiral gravity.

Chiral gravity in three dimensions

Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic \mu due to negative-energy massive gravitons. However at the critical value \mu\ell=1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by \ell M=J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c_L,c_R)=(0,3\ell /G).

The modified Bargmann-Wigner formalism for bosons of spin 1 and 2

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2J+1) theory are found. Next, we introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed.

Modified Bargmann-Wigner Formalism (Bosons of Spin 1 and 2)

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and theWeinberg 2(2J+1) theory are found. Next, we introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed.

Chiral gravity as a covariant formulation of massive gravity

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 Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level.

Chiral gravity in higher dimensions

We construct a chiral theory of gravity in seven and eight dimensions, which is equivalent to Einstein–Cartan theory using fewer variables. In these dimensions, we can construct such higher-dimensional chiral gravity because of the existence of the gravitational instanton. The octonionic-valued variables in the theory represent the deviation from the gravitational instanton, and from their non-associativity, prevent the theory being SO(n) gauge invariant. Still the chiral gravity holds G2 (7D), and spin(7) (8D) gauge symmetry.

Massive torsion modes, chiral gravity and the Adler–Bell–Jackiw anomaly

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler–Bell–Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin-½ particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition, it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel–Jacobson–Smolin action of chiral gravity in four dimensions.

Fundamental constants in effective theory

There is a discussion between L. B. Okun, G. Veneziano and M. J. Duff, concerning the number of fundamental dimensionful constants in physics (physics/0110060). They advocated correspondingly 3, 2 and 0 fundamental constants. Here we consider this problem on example of the effective relativistic quantum field theory, which emerges in the low energy corner of quantum liquids and which reproduces many features of our physics including chiral fermions, gauge fields and dynamical gravity.