Auxiliary Tensor Field Research Articles

Analysis of unitarity in conformal quantum gravity

We perform a canonical quantization of Weyl’s conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth-order theory to second-order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a Becchi–Rouet–Stora–Tyutin (BRST) construction that includes Faddeev–Popov ghost fields corresponding to Weyl transformations. This second-order formulation allows the formal tools of operator-based quantum field theory to be applied to quadratic gravity for the first time. Using the Kugo–Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.

Auxiliary tensor fields for Sp(2, ℝ) self-duality

The coset Sp(2, ℝ)/U(1) is parametrized by two real scalar fields. We generalize the formalism of auxiliary tensor (bispinor) fields in U(1) self-dual nonlinear models of abelian gauge fields to the case of Sp(2, ℝ) self-duality. In this new formulation, Sp(2, ℝ) duality of the nonlinear scalar-gauge equations of motion is equivalent to an Sp(2, ℝ) invariance of the auxiliary interaction. We derive this result in two different ways, aiming at its further application to supersymmetric theories. We also consider an extension to interactions with higher derivatives.

Unifying the PST and the auxiliary tensor field formulations of 4D self-duality

We unify the Lorentz- and O(2) duality-covariant approach to 4D self-dual theories by Pasti, Sorokin and Tonin (PST) with the formulation involving an auxiliary tensor field. We present the basic features of the new hybrid approach, including symmetries of the relevant generalized PST action. Its salient peculiarity is the unique form of the realization of the PST gauge symmetries. The corresponding transformations do not affect the auxiliary tensor field, which guarantees the self-duality of the nonlinear actions in which the O(2) invariant interactions are constructed out of the tensor field.

One-loop divergences in massive gravity theory

The one-loop divergences are calculated for the recently proposed ghost-free massive gravity model, where the action depends on both metric and external tensor field f. The non-polynomial structure of the massive term is reduced to a more standard form by means of auxiliary tensor field, which is settled on-shell after quantum calculations are performed. As one should expect, the counter-terms do not reproduce the form of the classical action. Moreover, the result has the form of the power series in f.

Ordinary-derivative formulation of conformal low-spin fields

Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field. With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term. Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries. Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories.

A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds

We investigate the Brown-York stress tensor for curvature-squared theories. This requires a generalized Gibbons-Hawking term in order to establish a well-posed variational principle, which is achieved in a universal way by reducing the number of derivatives through the introduction of an auxiliary tensor field. We examine the boundary stress tensor thus defined for the special case of ‘massive gravity’ in three dimensions, which augments the Einstein-Hilbert term by a particular curvature-squared term. It is shown that one obtains finite results for physical parameters on AdS upon adding a ‘boundary cosmological constant’ as a counterterm, which vanishes at the so-called chiral point. We derive known and new results, like the value of the central charges or the mass of black hole solutions, thereby confirming our prescription for the computation of the stress tensor. Finally, we inspect recently constructed Lifshitz vacua and a new black hole solution that is asymptotically Lifshitz, and we propose a novel and covariant counterterm for this case.

New approach to nonlinear electrodynamics: Dualities as symmetries of interaction

The duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields is considered. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is represented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics admit a simple off-shell characterization as symmetry properties of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality-symmetric Lagrangians, an alternative representation with the auxiliary scalar field is introduced and new explicit examples of such systems are found.

N=3 supersymmetric Born–Infeld theory

We construct an off-shell N=3 supersymmetric extension of the abelian D=4 Born–Infeld action starting from the action of supersymmetric Maxwell theory in N=3 harmonic superspace. A crucial new feature of the N=3 super BI action is that its interaction part contains only terms of the order 4 k in the N=3 superfield strengths. The correct component bosonic BI action arises as the result of elimination of auxiliary tensor field which is present in the off-shell N=3 vector multiplet in parallel with the gauge field strength. In this new Legendre-type representation, the bosonic BI action is fully specified by a real function of the single variable quartic in the auxiliary tensor field. The generic choice of this function amounts to a wide set of self-dual nonlinear extensions of the Maxwell action. All of them admit an off-shell N=3 supersymmetrization.