Chiral Gravity Research Articles

Free fields for chiral 2D dilaton gravity

We give an explicit canonical transformation which transforms a generic chiral 2D dilaton gravity model into a free field theory.

NONLINEAR REALISATIONS AND EMBEDDINGS OF QUANTUM ALGEBRAS

A review is given of BRST mechanisms through which theories carrying realisations of nonlinear gauge-algebra representations may also be viewed as realizing embeddings into larger gauge algebras. This process generalizes the familiar non-linear realisations of spontaneously-broken Lie-algebra gauge symmetries to ssupersymmetric and higher-spin chiral quantum gravity models.

Chiral fermions coupled to chiral gravity

Using a purely imaginary translational Chern-Simons term as a generating function, a chiral reformulation of gravity à la Ashtekar is achieved. It is a crucial advantage of our Clifford algebra approach that the coupling to the chiral Dirac and the Rarita-Schwinger fields arises from the same translational Chern-Simons term, now evaluated “on shell”.

Lorentz anomaly and 1+1-dimensional radiating black holes

The radiation from the black holes of a 1+1-dimensionial chiral quantum gravity model is studied. Most notably, a non-trivial dependence on a renormalization parameter that characterizes the anomaly relations is uncovered in an improved semiclassical approximation scheme; this dependence is not present in the naive semiclassical approximation.

Background gauge invariance in the anti-field formalism for theories with open gauge algebras

We show that any BRST-invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the anti-field formalism, then the effective action possesses a local background gauge invariance. The presence of anti-fields (BRST sources) is necessary. As an example we analyse chiral gravity.

Non-locally regularized antibracket-antifield formalism and anomalies in chiral W3 gravity

The non-local regularization method, recently proposed by Evans et al., and Kleppe and Woodward, is extended to general gauge theories by reformulating it along the ideas of the antibracket-antifield formalism. From the interplay of both frameworks a fully regularized version of the field-antifield (FA) formalism arises, being able to deal with higher order loop corrections and to describe higher order loop contributions to the BRST anomaly. The quantum master equation, considered in the FA framework as the quantity parametrizing BRST anomalies, is argued to be incomplete at two and higher order loops and conjectured to reproduce only the one-loop corrections to the h ̵ p anomaly generated by the addition of O( h ̵ k) , k < p, counterterms. Chiral W 3 gravity is used to exemplify the non-locally regularized FA formalism. First, the regularized one-loop quantum master equation is used to compute the complete one-loop anomaly. Its two-loop order, however, is shown to reproduce only the modification to the two-loop anomaly produced by the addition of a suitable one-loop counterterm, thereby providing an explicit verification of the previous statement for p = 2. The well-known universal two-loop anomaly, instead, is alternatively obtained from the BRST variation of the non-locally regulated effective action. Incompleteness of the quantum master equation is thus concluded to be a consequence of a naive derivation of the FA BRST Ward identity.

Simplifications in lagrangian BV quantization exemplified by the anomalies of chiral W3 gravity

The Batalin-Vilkovisky (BV) formalism is a useful framework to study gauge theories. We summarize a simple procedure to find a gauge-fixed action in this language and a way to obtain one-loop anomalies. Calculations involving the antifields can be greatly simplified by using a theorem on the antibracket cohomology. The latter is based on properties of a “Koszul-Tate differential”, namely its acyclicity and nilpotency. We present a new proof for this acyclicity, respecting locality and covariance of the theory. This theorem then implies that consistent higher ghost terms in various expressions exist, and it avoids tedious calculations. This is illustrated in chiral W 3 gravity. We compute the one-loop anomaly without terms of negative ghost number. Then the mentioned theorem and the consistency condition imply that the full anomaly is determined up to local counterterms. Finally we show how to implement background charges into the BV language in order to cancel the anomaly with the appropriate counterterms. Again we use the theorem to simplify the calculations, which agree with previous results.

Solvable extensions of two-dimensional gravity

The authors briefly review results for chiral W3 gravity and chiral N-extended supergravity in two dimensions. They present explicit, all-loop expressions for the effective actions of these theories They are obtained by renormalization of the leading terms of the corresponding induced actions. They discuss how the latter can be obtained by imposing suitable constraints on the currents of an Sl(3, R) or Osp(N/2) WZWN model.

Kac-Moody structure of chiral gravity in the light-cone gauge

We study the residual symmetry SL (2, R ) ⊗U(1) of the chiral gravity in the light-cone gauge. Quantum gravitational effects renormalize the Kac-Moody central charge and introduce, through the Lorentz anomaly, an arbitrary parameter. Due to the presence of this free parameter the Kac-Moody central charge has no forbidden range of values, and the strong gravity regime is open to investigations.

Chiral gravity in two dimensions

It is shown that conformal matter with c L ≠ c R can be consistently coupled to two-dimensional “frame” gravity. The theory is quantized, following David, and Distler and Kawai, using the derivation of their ansatz due to Mavromatos and Miramontes, and D'Hoker and Kurzepa. New super-selection rules are found by requiring SL(2, C ) invariance of correlation functions on the plane. There is no analogue of the c=1 barrier found in non-chiral and non-critical strings. A non-critical heterotic string is constructed — it has 744 states in its spectrum, transforming in the adjoint representation of (E 8) 3. Correlation functions are calculated in this example.

SIEGEL'S CHIRAL BOSON AND THE CHIRAL SCHWINGER MODEL

Siegel's proposal for a Lagrangian formulation of a chiral boson is analyzed by applying recent results on 2d chiral quantum gravity, A model is derived whose solution consists of a massive scalar and two massless chiral scalars. Therefore it is a minimally bosonized two-fermion chiral Schwinger model.

Quantum w 3 gravity in the chiral gauge

We analyze the quantum theory of W 3 gravity in the chiral gauge, coupled to scalar fields or to W 3 matter. We evaluate the effective action through 3-loop order, using both Feynman diagrams and OPE methods. We exhibit two distinct Ward identities for the W 3 symmetry, in which new terms appear due to the essential non-linearities in the theory. The relation with KPZ's program for chiral gravity and its extension to W 3 gravity are briefly discussed.

Anomalous aspects of chiral quantum gravity in two dimensions.

We study anomalous aspects of a theory in which a set of chiral fermions is coupled to gravity in two dimensions. We first give a perturbative derivation of the effective action in the conformal gauge. From this the complete fermion propagator is obtained in the path-integral formalism, and also from operator solutions. The fermion is shown to acquire an anomalous dimension purely by quantum effects, i.e., through interactions with scalars which are dynamical only after quantization. The renormalization of the theory is also discussed.

ISO(2,1) chiral models and quantum gravity in 2 + 1 dimensions

We study gravity in 2 + 1 dimensions on the manifold M = D 2 × ℝ. A specific choice of boundary conditions leads to an equivalence of the system with a chiral Wess-Zumino-Novikov-Witten model associated with the group ISO(2,1). The model is written on the boundary S 1 × ℝ of M. We find induced representations of the corresponding Kac-Moody and Virasoro algebras with zero Virasoro anomaly.

Chiral quantum gravity in two dimensions

We study a theory of chiral fermions coupled to quantum gravity in two dimensions. It is shown that the theory can be made unitary and contains two massless excitations which correspond to the Weyl and the Lorentz degrees of freedom. We compare this model with the chiral Schwinger model and reveal some remarkable similarities between them, although the respective mechanisms which render both theories consistent are slightly different.