Field Redefinition Research Articles

Quantum stability of a new Proca theory

The construction of general derivative self-interactions for a massive Proca field relies on the well-known condition for constrained systems of having a degenerate Hessian. The nature of the existing constraints algebra will distinguish among different classes of interactions. Proca-Nuevo interactions enjoy a non-trivial constraint by mixing terms of various order whereas Generalized Proca interactions satisfy the degeneracy condition order by order for each individual Lagrangians. In both cases the vector field propagates at most three degrees of freedom. It has been shown that the scattering amplitudes of Proca-Nuevo arising at the tree level always differ from those of the Generalized Proca, implying their genuinely different nature and a lack of relation by local field redefinitions. In this work, we show the quantum stability of the Proca-Nuevo theory below a specific UV cut-off. Although Proca-Nuevo and Generalized Proca are different inherently in their classical structure, both have the same high energy behaviour when quantum corrections are taken into account. The arising counter terms have the exact same structure and scaling. This might indicate that whatever UV completion they may come from, we expect it to be of similar nature.

Correspondence between momentum-dependent relaxation time and field redefinition of relativistic hydrodynamic theory

In this article a correspondence has been established between the out of equilibrium system dissipation and the thermodynamic field redefinition of the macroscopic variables through the momentum dependent relaxation time approximation (MDRTA) solution of relativistic transport equation. Here, it has been shown that the out of equilibrium thermodynamic fields are not uniquely defined and are subjected to include dissipative effects from the medium. A second order relativistic hydrodynamic theory has been developed including such dissipative effects. The necessary conditions for developing a hydrodynamic theory has been fulfilled, (i) the thermodynamic identities incorporating such redefined fields have been shown to conserve the energy-momentum tensor perfectly under MDRTA, (ii) the non-negativity of entropy production remains unaffected by the inclusion of such dissipative contributions in hydro fields as long as the independent transport coefficients remain positive.

Background Independence and Field Redefinitions in Quantum Gravity

Background Independence and Field Redefinitions in Quantum Gravity

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ξ2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ2 reduces the action to a local two-derivative theory with a ξ2-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory

In previous work, we showed that in loop quantum cosmology of scalar-tensor theory (STT) with the holonomy correction the background equations of motion in the Jordan frame have two branches, i.e., the ${b}_{+}$ branch and the ${b}_{\ensuremath{-}}$ branch. In the low-energy limit, the ${b}_{+}$ branch of the equations of motion reproduce the equations of motion of classical STT, while the ${b}_{\ensuremath{-}}$ branch of equations of motion do not reproduce the classical equations. In this paper, we investigate cosmological dynamics in an expanding universe whose background is described by the ${b}_{\ensuremath{-}}$ branch of equations of motion of STT, and we especially focus on the dynamics of the perturbations in the low-energy limit because it is most relevant to the current observational range. First, we show that the low-energy limit of the ${b}_{\ensuremath{-}}$ branch of equations of motion can be a stable attractor in the expansion phase of a universe. Then, we find a low-energy effective Hamiltonian on the spatially flat Friedmann-Robertson-Walker background. The background part of this Hamiltonian can yield the low-energy limit of the ${b}_{\ensuremath{-}}$ branch of equations, and this Hamiltonian consists of constraints whose constraint algebra is different from the classical case but also closed up to arbitrary order of perturbations. Remarkably, we find that this Hamiltonian can be transformed into the Hamiltonian of the Einstein frame by field redefinitions different from the classical case. Moreover, we also develop the linear cosmological perturbation theory and apply it to study the slow-roll inflation in this context. Finally, we study a specific model of STT. In this model, a contracting universe described by classical STT in the remote past can pass through the bounce and evolve into an expanding universe whose background dynamics is described by the ${b}_{\ensuremath{-}}$ branch of equations of motion. It is also shown that the slow-roll inflation can take place in this case, and the spectral indices of the slow-roll inflation agree well with the observations. The results in this paper indicate that there exists an alternative consistent theory which is different from the classical theory in the low-energy limit of loop quantum STT.

Absence of covariant singularities in pure gravity

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.

Wavefunction of the universe: Reparametrization invariance and field redefinitions of the minisuperspace path integral

We consider the Hartle–Hawking wavefunction of the universe defined as a Euclidean path integral that satisfies the “no-boundary proposal.” We focus on the simplest minisuperspace model that comprises a single scale factor degree of freedom and a positive cosmological constant. The model can be seen as a non-linear σ-model with a line-segment base. We reduce the path integral over the lapse function to an integral over the proper length of the base and use diffeomorphism-invariant measures for the ghosts and the scale factor. As a result, the gauge-fixed path integral is independent of the gauge. However, we point out that all field redefinitions of the scale factor degree of freedom yield different choices of gauge-invariant path-integral measures. For each prescription, we compute the wavefunction at the semi-classical level and find a different result. We resolve in each case the ambiguity in the form of the Wheeler–DeWitt equation at this level of approximation. By imposing that the Hamiltonians associated with these possibly distinct quantum theories are Hermitian, we determine the inner products of the corresponding Hilbert spaces and find that they lead to a universal norm, at least semi-classically. Quantum predictions are thus independent of the prescription at this level of approximation. Finally, all wavefunctions of the Hilbert spaces of the minisuperspace model we consider turn out to be non-normalizable, including the no-boundary states.

Hidden relations of central charges and OPEs in holographic CFT

It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓeff∂a/∂ℓeff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Logarithmic corrections to the entropy of non-extremal black holes in mathcal{N} = 1 Einstein-Maxwell supergravity

We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for “non-minimal” mathcal{N} = 1 Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordström and Schwarzschild black holes in “non-minimal” mathcal{N} = 1, d = 4 Einstein-Maxwell supergravity.

On massive spin-2 in the Fradkin-Vasiliev formalism. II. General massive case

In this work we apply the Fradkin-Vasiliev formalism based on the frame-like gauge invariant description of the massive and massless spin 2 to the construction of the cubic interactions vertices for massive spin 2 self-interaction as well as its gravitational interaction. In the first case we show that the vertex can be reduced (by field redefinitions) to the set of the trivially gauge invariant terms. There are four such terms which are not equivalent on-shell and do not contain more than four derivatives. Moreover, one their particular combination reproduces the minimal (with no more than two derivatives) vertex. As for the gravitational vertex, we show that due to the presence of the massless spin 2 there exist two abelian vertices (besides the three trivially gauge invariant ones) which are not equivalent to any trivially gauge invariant terms and can not be removed by field redefinitions. Moreover, their existence appears to be crucial for the possibility to reproduce the minimal two derivatives vertex.

Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity

We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4 parity doublet in $D=2+1$. They are of higher order in derivatives and are described by a totally symmetric rank-4 tensor without extra auxiliary fields. Despite the higher derivatives they are ghost free. We find gauge invariant field combinations which allow us to show that the canonical structure of the spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1) counterpart after field redefinitions. For $s=1$, 2, 3, 4, the spin-$s$ self-dual models of order $2s\ensuremath{-}1$ and the doublet models of order $2s$ can be written in terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted conformal higher spin symmetry as a principle for defining linearized topologically massive gravity and linearized ``new massive gravity'' for arbitrary integer spins. A key role in our approach is played by the fact that the Cotton tensor in $D=2+1$ has only two independent components for any integer spin.

Manifest spacetime supersymmetry and the superstring

The algebra of spacetime supersymmetry generators in the RNS formalism for the superstring closes only up to a picture-changing operation. After adding non-minimal variables and working in the “large” Hilbert space, the algebra closes without picture-changing and spacetime supersymmetry can be made manifest. The resulting non-minimal version of the RNS formalism is related by a field redefinition to the pure spinor formalism.

O(9,9) symmetry of NS-NS couplings at order α′3

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $\alpha'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

Closed string deformations in open string field theory. Part II. Superstring

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the A∞ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new A∞ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

Inflation with R (αβ) terms in the Palatini formulation

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation.As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case R + α R 2 that has been studied earlier: the tensor-to-scalar ratio r can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, r can be suppressed by at most a factor of 2/9, and the change in the scalar spectral index n s can be large.

Poisson gauge theory

The Poisson gauge algebra is a semi-classical limit of complete non- commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding algebra of gauge symmetries. The proposed model is designed to investigate the semi-classical features of the full non-commutative gauge theory with coordinate dependent non-commutativity Θab(x), especially whose with a non-constant rank. We derive the expression for the covariant derivative of matter field. The commutator relation for the covariant derivatives defines the Poisson field strength which is covariant under the Poisson gauge transformations and reproduces the standard U(1) field strength in the commutative limit. We derive the corresponding Bianchi identities. The field equations for the gauge and the matter fields are obtained from the gauge invariant action. We consider different examples of linear in coordinates Poisson structures Θab(x), as well as non-linear ones, and obtain explicit expressions for all proposed constructions. Our model is unique up to invertible field redefinitions and coordinate transformations.

On massive spin-3/2 in the Fradkin–Vasiliev formalism

One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated by Boulanger et al (2018 J. High Energy Phys. JHEP07(2018)021). The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory. Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin–Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-3/2 field so we complete the investigation started by Buchbinder et al (2014 Eur. Phys. J. C 74 3153) relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-3/2.

Duality-invariant extensions of Einstein-Maxwell theory

We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.

O(25,\xa025) symmetry of bosonic string theory at order alpha '^2

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order alpha '^2, up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

On NS-NS couplings at order [formula omitted

Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories at order α′3, the NS-NS couplings have been found in a particular scheme which has 445 couplings in 15 different structures. In this paper, using a field redefinition, we write them in terms of 251 couplings which appear in 9 different structures. The 9 structures involve only Riemann curvature, Hαβμ and ∇αHβμν. The number of couplings in the structures R4, H8, H6R, H4R2, H2R3 are 2, 2, 1, 7, 22, respectively, and the number of couplings in the structures (∇H)4, (∇H)2R2, (∇H)2H4, (∇H)2H2R are 12, 22, 77, 106, respectively. The new couplings are also fully consistent with the sphere-level S-matrix element of four NS-NS vertex operators.