We present several Galileo invariant Lagrangians, which are invariant against Poincare transformations defined in one higher (spatial) dimension. Thus these models, which arise in a variety of physical situations, provide a representation for a dynamical (hidden) Poincare symmetry. The action of this symmetry transformation on the dynamical variables is nonlinear, and in one case involves a peculiar field-dependent diffeomorphism. Some of our models are completely integrable, and we exhibit explicit solutions.
We consider a description of membranes by (2,1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as others related to them, admit a peculiar diffeomorphism symmetry, where the transformation rule for coordinates involves the fields. The symmetry algebra coincides with that of the Poincare group in one higher dimension. Therefore, these models provide a nonlinear representation for a dynamical Poincare group.
In the first order form, the model considered by Strobl presents, besides local Lorentz and diffeomorphism invariances, an additional local non-linear symmetry. When the model is realized as a Poincaré gauge theory according to the procedure outlined in Refs.[1,2], the generators of the non-linear symmetry are responsible for the ``nasty constraint algebra''. We show that not only the Poincaré gauge theoretic formulation of the model is not the cause of the emerging of the undesirable constraint algebra, but actually allows to overcome the problem. In fact one can fix the additional symmetry w…
I examine the relationship between $(d+1)$-dimensional Poincaré metrics and $d$-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries, in general relativity and in gauge-gravity duality, as follows: (1: Ambient Construction) I draw from the remarkable work by Fefferman and Graham (1985, 2012) on conformal geometry, in order to prove two propositions and a theorem that characterise the classes of diffeomorphisms that qualify as gravity-invisible. I define natural notions of gra…
We analyze possible local extensions of the Poincaré symmetry in light-cone gravity in four dimensions. We use a formalism where we represent the algebra on the two physical degrees of freedom, one with helicity $2$ and the other with helicity $-2$. The representation is non-linearly realized and one of the light-cone momenta is the Hamiltonian, which is hence a non-linear generator of the algebra. We find that this can be locally realized and the Poincaré algebra extended to the BMS symmetry without any reference to asymptotic limits.
The characterization of the DBI action of a Dp-brane using the generalized geometry is discussed. It is shown that the DBI action is invariant under the diffeomorphism and B-transformation of the generalized tangent bundle of the target space. The symmetry is realized non-linearly on the fluctuation of the D-brane.
We calculate the time evolution of the entanglement entropy in a 1+1 CFT with a holographic dual when there is a localized left-moving packet of energy density. We find the gravity result agrees with a field theory result derived from the transformation properties of Rényi entropy. We are able to reproduce behavior which qualitatively agrees with CFT results of entanglement entropy of a system subjected to a local quench. In doing so we construct a finite diffeomorphism which tales three-dimensional anti-de Sitter space in the Poincaré patch to a general solution, generalizing the diffeomorphi…
A new linear system is constructed for Poincaré supergravities in two dimensions. In contrast to previous results, which were based on the conformal gauge, this linear system involves the topological world sheet degrees of freedom (the Beltrami and super-Beltrami differentials). The associated spectral parameter likewise depends on these and is itself subject to a pair of differential equations, whose integrability condition yields one of the equations of motion. These results suggest the existence of an extension of the Geroch group mixing propagating and topological degrees of freedom on the…
It is shown that algebra of quantum space of the title of the present paper may be realized on usual unphysical Minkowskii one. Equations of field theory and there solutions are discussed. Solution equations of particle motion are obtained in implicit form from the classical ones.
We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan-Paton factor is given by a trace over elements of Poincaré algebra and Iwahori-Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan-Paton factor and show that an S-matrix functional f…
Following the general method discussed in Refs.[1,2], Liouville gravity and the 2 dimensional model of non-Einstenian gravity ${\cal L} \sim curv^2 + torsion^2 + cosm. const.$ can be formulated as ISO(1,1) gauge theories. In the first order formalism the models present, besides the Poincaré gauge symmetry, additional local symmetries. We show that in both models one can fix these additional symmetries preserving the ISO(1,1) gauge symmetry and the diffeomorphism invariance, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the ISO(1,1) algebra. After the …
We present evidence that there is a 4D model that satisfies the conditions of renormalizability and diffeomorphism invariance simultaneously at the 2-loop level. The traceless mode is treated perturbatively, while the conformal mode can be managed exactly. The two conditions constrain the theory strongly and determine the measure of the gravitational field uniquely. Quantum corrections of the cosmological constant are computed in part to 3-loop diagrams. The method to remove the negative-metric states is also discussed from the viewpoint of diffeomorphism invariance in analogy to the $R_ξ$ gau…
A dynamical symmetry, as well as special diffeomorphism algebras generalizing the Witt-Virasoro algebra, related to Poincaré-invariance and crucial with regard to quantisation, questions of integrability, and M(atrix) theory, are found to exist in the theory of relativistic extended objects of any dimension.
A systematic analysis of the symmetries of topological 3D gravity with torsion and a cosmological term, in the first order formalism, has been performed in details - both in the hamiltonian and lagrangian formalisms. This illuminates the connection between the symmetries of curved spacetime (diffeomorphisms plus local Lorentz transformations) with the Poincare gauge transformations. The Poincare gauge symmetries of the action are shown to be inequivalent to its gauge symmetries. Finally, the complete analysis is compared with the metric formulation where the diffeomorphism symmetry is shown to…
The gauging of the q-Poincaré algebra of ref. hep-th 9312179 yields a non-commutative generalization of the Einstein-Cartan lagrangian. We prove its invariance under local q-Lorentz rotations and, up to a total derivative, under q-diffeomorphisms. The variations of the fields are given by their q-Lie derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is shown to close with field dependent structure functions. The equations of motion are found, generalizing the Einstein equations and the zero-torsion condition.
We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler compared to the existing formulations of noncommutative gravity.
We pursue the study of the type IIB matrix model as a constructive definition of superstring. In this paper, we justify the interpretation of space-time as distribution of eigenvalues of the matrices by showing that some low energy excitations indeed propagate in it. In particular, we show that if the distribution consists of small clusters of size $n$, low energy theory acquires local SU(n) gauge symmetry and a plaquette action for the associated gauge boson is induced, in addition to a gauge invariant kinetic term for a massless fermion in the adjoint representation of the SU(n). We finally …
We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated to SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the `broken phase' can be reconstructed…
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented…
In all the odd dimensions which allow Majorana spinors, we consider a gravitational Lagrangian possessing local Poincare invariance and given by the dimensional continuation of the Euler density in one dimension less. We show that the local supersymmetric extension of this Lagrangian requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. By maximal, we mean that in the right hand side of the anticommutator of the Majorana super charge appear all the possible central charges. The resulting action defines a Chern-Simons gauge theory for the maximal extension of the s…
We demonstrate the one-to-one correspondence between reparametrization invariant effective actions for relativistic p-branes in flat target space and effective actions for transverse brane perturbations with non-linearly realized Poincaré symmetry. Starting with an action with non-linearly realized symmetry we construct the corresponding reparametrization invariant action by introducing Stückelberg fields. They combine with the transverse modes to form a Lorentz vector. The manifest Lorentz symmetry of the reparametrization invariant action follows directly from the non-linearly realized Loren…
The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical quantities. For the sake of simplicity, the case of a single $c$ is selected and chosen mass-independent if masslessness is not realized, this with the aim of expressing the effect of an infinitesimal change in $c$ on the computed observables. This change is found to be expressible in terms of an equation involving a vector field $V$ on the action's space $M$ (c…
The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita and Takesaki) of the algebraic formulation of QFT has an interesting nontrivial chiral generalization to the diffeomorphisms of the circle. Combined with recent ideas on algebraic (d-1)-dimensional lightfront holography, these diffeomorphisms turn out to be images of ``fuzzy'' acting groups in the original d-dimensional (massive) QFT. These actions do not r…
We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving di…
We discuss a generalization of Chern-Simons theory in three dimensions based on Leibniz (or Loday) algebras, which are generalizations of Lie algebras. Special cases of such theories appear in gauged supergravity, where the Leibniz algebra is defined in terms of the global (Lie) symmetry algebra of the ungauged limit and an embedding tensor. We show that the Leibniz algebra of generalized diffeomorphisms in exceptional field theory can similarly be obtained from a Lie algebra that describes the enhanced symmetry of an `ungauged phase' of the theory. Moreover, we show that a `topological phase'…
We argue that Poincaré symmetry can be implemented in NCFT if we allow the parameter of noncommutitive deformation $θ^{μν}$ to change as a two-tensor under the corresponding space-time symmetry. The implementation is consistent with the definition of $θ^{μν}$ in terms of space-time coordinates and with the Moyal star product. Inspired from the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of $θ^{μν}$ in such a way that the new transformation define a symmetry of the theory. F…
It is shown that the previously noticed internal dynamical $SO(D-1)$ symmetry arXiv:1003.5189 for relativistic M-branes moving in $D$-dimensional space-time is naturally realized in the (extended by powers of $\frac{1}{p_+}$) enveloping algebra of the Poincaré algebra.
The Polymer Quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such Polymer Quantization is the subgroup $\mbox{SDiff}(\mathbb{R}^4)$ which is a subgroup of $\mbox{Diff}(\mathbb{R}^4)$ formed by spatial volume preserving diffeomorphisms. In consequence, thi…
The key ingredient for lattice regularized quantum gravity is diffeomorphism symmetry. We formulate a lattice functional integral for quantum gravity in terms of fermions. This allows for a diffeomorphism invariant functional measure and avoids problems of boundedness of the action. We discuss the concept of lattice diffeomorphism invariance. This is realized if the action does not depend on the positioning of abstract lattice points on a continuous manifold. Our formulation of lattice spinor gravity also realizes local Lorentz symmetry. Furthermore, the Lorentz transformations are generalized…
We propose a lattice counterpart of diffeomorphism symmetry in the continuum. A functional integral for quantum gravity is regularized on a discrete set of space-time points, with fermionic or bosonic lattice fields. When the space-time points are positioned as discrete points of a continuous manifold, the lattice action can be reformulated in terms of average fields within local cells and lattice derivatives. Lattice diffeomorphism invariance is realized if the action is independent of the positioning of the space-time points. Regular as well as rather irregular lattices are then described by…
We show that locally Lorentz invariant, third order, topological massive gravity can not be broken down neither to the local diffeomorphism subgroup nor to the rigid Poincaré group. On the other hand, the recently formulated, locally diffeomorphism invariant, second order massive triadic (translational) Chern-Simons gravity breaks down on rigid Minkowski space to a double massive spin-two system. This flat double massive action is the uniform spin-two generalization of the Maxwell-Chern-Simons-Proca system which one is left with after U(1) abelian gauge invariance breaks down in the presence o…
Quantum field theory - our basic framework for describing all non-gravitational physics - conflicts with general relativity: the latter precludes the standard definition of the former's essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincare charges, and in particular any compactly-supported operator, in flat-spacetime quantum field theory must be gravitationally dre…
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of $g$. Motivated by elasticity theory, we introduce a Lagrangian expressed algebraically (without differentiations) via our pair of metrics. Analysis of the resulting nonlinear field equations produces three main results. Firstly, we show that for Ricci-flat manifolds our linearised field equations are Maxwell's equations in the Lorenz gauge with exact current…
Recently Gliozzi has shown that, under certain conditions, it is possible to derive the Dirac-Born-Infeld action for an abelian gauge field of a D-brane. Also, the action turns out to be invariant with respect to a non-linear realization of the full Poincaré group. A crucial role is played by the transformation properties of the gauge field under the non-linear realization. The aim of this note is to point out that these transformation properties are derived directly from the gauge fixing of the diffeomorphisms of the brane and the necessary compensating reparametrization when one performs a L…
In the presence of a confining flux tube between a pair of sources the vacuum is no longer Poincare' invariant. This symmetry is nonlinearly realized in the effective string action. A general method for finding a large class of Lorentz invariant contributions to the action is described. The relationship between this symmetry and diffeomorphism invariance is further investigated.
We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a Poincare invariant 2-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory. Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for spacetimes with non-constant curvature backgrounds, by using the d…
We analyse the conservation laws in the gauge gravity theory which are derived for the general class of gravitational models with the action invariant under the local Poincare and the diffeomorphism group. The consistent Noether-Lagrange formalism is developed, revealing the important role of the auxiliary Goldstone and Stueckelberg fields, with the help of which we construct the composite gauge fields that have a clear geometrical and physical meaning.
A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. Among the applications studied are the reduction to string theory, which may be understood in terms of the phase space and constraints, and the interpretation of physical,zero-energy states. A matrix regularization is defined as in the light cone gauged fixed theory but there are difficulties implementing all the gauge symmetries. The problem involves the non-area-preserving diffeomorphisms which are realized non-linearly in the clas…
We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R due to the deformation. According to this symmetry, there are two descriptions to describe the classical dynamics of the system, 1) the SL(2,R)_L description and 2) the enhanced U(1)_R description. In the former 1), we show that the Yangian symmetry is realized by improving the SL(2,R)_L Noether c…
We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions $D$, with a particular emphasis on the case $D=5$. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS$_5$, which is realized non linearly, contains a four-fold family of angle-dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions $D…
We present a manifestly local, diffeomorphism invariant and locally Poincare invariant formulation of vacuum energy sequestering. In this theory, quantum vacuum energy generated by matter loops is cancelled by auxiliary fields. The auxiliary fields decouple from gravity almost completely. Their only residual effect is an a priori arbitrary, finite contribution to the curvature of the background geometry, which is radiatively stable. Its value is to be determined by a measurement, like the finite part of any radiatively stable UV-sensitive quantity in quantum field theory.
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincaré invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of …
In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter inva…
