This article reports on how diagrammatic identities of Yang--Mills theory translate to diagrammatics for pure gravity. For this, we consider the Einstein--Hilbert action and follow the approach of Capper, Leibbrandt, and Medrano and expand the inverse metric density around the Minkowski metric. By analogy to Yang--Mills theory, cancellation identities are constructed for the graviton as well as the ghost vertices up to the valency of six.
We discuss the on-shell diagrammatic representation of theories less special than maximally supersymmetric Yang-Mills. In particular, we focus on planar $\mathcal{N}\,\le\,2$ gauge theories, including pure Yang-Mills. For such a class of theories, the on-shell diagrammatics is endowed with a decoration which carries the information on the helicity of the coherent states. In the first part of the paper we extensively discuss the properties of this decorated diagrammatics. Particular relevance have the helicity flows that the decoration induces on the diagrams, which allows to identify the diffe…
We confirm recently proposed theorems for the structure of next-to-soft corrections in gauge and gravity theories using diagrammatic techniques, first developed for use in QCD phenomenology. Our aim is to provide a useful alternative insight into the next-to-soft theorems, including tools that may be useful for further study. We also shed light on a recently observed double copy relation between next-to-soft corrections in the gauge and gravity cases.
We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general graph-theoretical formulation for the tree-level maximally-helicity-violated gravity amplitudes. Furthermore, we use the link to prove two identities for half-soft functions of gravity amplitudes. Finally we recast the diagrammatic formulation of one-loop rational part of $\mathcal{N}=4$ supergravity into a matrix form.
In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.
In this work we construct charged thin-shell Lorentzian wormholes in dilaton gravity. The exotic matter required for the construction is localized in the shell and the energy conditions are satisfied outside the shell. The total amount of exotic matter is calculated and its dependence with the parameters of the model is analysed.
Off-shell processes do not preserve the Energy Momentum Tensor (EMT) in QFT. Fixing the EMT throughout off-shell processes, implies a graviton-like quantum field to emerge without dynamics. Its dynamics are generated through quantum corrections. This Fixed Off-Shell Energy Condition (FOSEC) implies the existence of a linear gravity-like theory, and in special cases the full Poincarè gauge theory. In this work it is shown that imposing the FOSEC in QFT implies the emergence of a viable quantum theory of gravity.
In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein-Hilbert action, the most general $L(g_{μν}, R^λ{}_{ναμ}, T^λ{}_{αβ}, Q_{α…
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF-theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our…
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of metric. Nevertheless, some terms can be included in the renormalization of Newton's constant. This ambiguity in the renormalization prescription is discussed.
We consider a collision of two dust thin shells with a high center-of-mass (CM) energy including their self-gravity in a Bañados-Teitelboim-Zanelli (BTZ) spacetime. The shells divide the BTZ spacetime into three domains and the domains are matched by the Darmois-Israel junction conditions. We treat only the collision of two shells which corotate with a background BTZ spacetime because of the junction conditions. The counterpart of the corotating shell collision is a collision of two particles with vanishing angular momenta. We compare the dust thin shell collision and the particle collision in…
A new way how to calculate the off-shell renormalization functions within the $R^2$-gravity has been proposed. The one-loop renormalization group equations in the approach suggested have been constructed. The behaviour of effective potential for an massless scalar field interacting with the quantum gravitational field has been analyzed in this approach.
We build spherically symmetric wormholes within the DGP theory. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions. We also show that it could exist solitonic shells charaterized by zero pressure and zero energy; thereafter we make some observations regarding their dynamic on the phase plane.
We investigate gravitational collapse of a spherically symmetric thin shell in the Einstein-Gauss-Bonnet (EGB) gravity. Under the recently proposed 4D limit, we find that the collapsing shell will be bounced back at a small radius, without forming a singularity. This bouncing behavior is similar to those of a test particle and a homogeneous spherical dust star, in accordance with the expectation that the Gauss-Bonnet term will modify the small scale behavior of the Einstein gravity. We analyze the causal structure of the dynamic spacetime that represents the bouncing process, finding that the …
In this work, we study the thin-shell wormholes in dRGT massive gravity. In order to joint two bulks of the spacetime geometry, we first derive junction conditions of the dRGT spacetime. This results the dynamics of the spherical thin-shell wormholes in the dRGT theory. We show that the massive graviton correction term of the dRGT theory in the Einstein equation is represented in terms of the effective anisotropic pressure fluid. However, if there is only this correction term, without invoking exotic fluids, we find that the thin-shell wormholes can not be stabilized. We then examine the stabi…
Mass inflation and thin shells in quasi-topological gravity
Institut für Theoretische Physik（理论物理研究所）；Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学与物理学院理论物理研究所）；Institute of Mathematics, Czech Academy of Sciences（捷克科学院数学研究所）
We study matching conditions for a spherically symmetric thin shell in Lovelock gravity which can be read off from the variation of the corresponding first-order action. In point of fact, the addition of Myers' boundary terms to the gravitational action eliminates the dependence on the acceleration in this functional and such that the canonical momentum appears in the surface term in the variation of the total action. This procedure leads to junction conditions given by the discontinuity of the canonical momentum defined for an evolution normal to the boundary. In particular, we correct existi…
We constructed thin-shell wormholes using the well-known "cut and paste" technique for static black holes sourced by an anisotropic fluid within the context of the Rastall gravity. Using the generalized Lanczos equations we explored the energy conditions at the wormhole's throat along with the traversability condition. We determined the stability regions when the wormhole configurations are surrounded by different bulk sources and obtained that the stability regions are considerably modified due to the non-trivial dependence of the Rastall parameter in the effective potential energy.
Rotating Thin Shells in Einstein-Gauss-Bonnet Gravity
University of Mississippi（密西西比大学）；Instituto de Telecomunicações - IUL（电信研究所 - IUL）；CENTRA, Departamento de Física do Instituto Superior Técnico (IST), Universidade de Lisboa（里斯本大学，高等技术学院物理系CENTRA）；Departamento de Matemática, ISCTE - Instituto Universitário de Lisboa（ISCTE - 里斯本大学学院数学系）
We study the effect of charge on gravitational collapse of inhomogeneous dust cloud in the Einstein, Gauss-Bonnet and Lovelock gravity. Dynamics of the collapsing shell is analyzed. The conditions for the occurrence of bounce during collapse are given. We also show that shell crossing occurs inevitably if the shell near the center is weakly charged.
Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the non-singular components of the bulk stress tensor on the sides of the thin shell. The equations are applied to spherically symmetric thin shells in vacuum. The shells are part of the vacuum, they carry no energy tensor. We cl…
It is proved that all thin-shell wormholes built from two identical regions of vacuum static, spherically symmetric space-times have a negative shell surface energy density in any scalar-tensor theory of gravity with a non-ghost massless scalar field and a non-ghost graviton.
The divergent part of the one-loop off-shell effective action is computed for a single scalar field coupled to the Ricci curvature of 2D gravity ($c ϕR$), and self interacting by an arbitrary potential term $V(ϕ)$. The Vilkovisky-DeWitt effective action is used to compute gauge-fixing independent results. In our background field/covariant gauge we find that the Liouville theory is finite on shell. Off-shell, we find a large class of renormalizable potentials which include the Liouville potential. We also find that for backgrounds satisfying $R=0$, the Liouville theory is finite off shell, as w…
We study scalarization of spherically symmetric neutral reflecting shells in the scalar-tensor gravity. We consider neutral static massless scalar fields non-minimally coupled to the Gauss-Bonnet invariant. We obtain a relation representing the existence regime of hairy neutral reflecting shells. For parameters unsatisfying this relation, the massless scalar field cannot exist outside the neutral reflecting shell. In the parameter region where this relation holds, we get analytical solutions of scalar field hairs outside neutral reflecting shells.
A given field theory action determines a set of field equations but other actions may yield equivalent field equations; if so they are on-shell equivalent. They may also be off-shell equivalent, being related by the elimination of auxiliary fields or by local field redefinitions, but this is not guaranteed, as we demonstrate by consideration of the linearized limit of 3D massive gravity models. Failure to appreciate this subtlety has led to incorrect conclusions in recent studies of the "Minimal Massive Gravity" model.
Off-shell equivalence in quantum field theory and gravity
Universidade Federal do Paraná（巴拉那联邦大学）；SISSA（的里雅斯特高等研究学校）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
The generalized Darmois--Israel formalism for Einstein--Gauss--Bonnet theory is applied to construct thin-shell Lorentzian wormholes with spherical symmetry. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions.
The gauge dependence of the conformal anomaly for spin 3/2 and spin 2 fields in non-conformal supergravities has been a long standing puzzle. In this Letter we argue that the `correct' gauge choice is the one that follows from requiring all terms that would imply a violation of the Wess-Zumino consistency condition to be absent in the counterterm, because otherwise the usual link between the anomaly and the one-loop divergence becomes invalid. Remarkably, the `good' choice of gauge is the one that confirms our previous result that a complete cancellation of conformal anomalies in D=4 can only …
We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We…
The parametrization and gauge dependencies of the one-loop counterterms on the mass-shell in the Einstein gravity are investigated. The physical meaning of the loop calculation results on the mass shell and the parametrization dependence of the renormgroup functions in the nonrenormalizable theories are discussed.
We investigate whether the classical equivalence of $f(R)$ gravity and its formulation as scalar-tensor theory still holds at the quantum level. We explicitly compare the corresponding one-loop divergences and find that the equivalence is broken by off-shell quantum corrections, but recovered on-shell.
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on the junction surface vanishes. So a spherical vacuum shell, containing no matter, arises as a boundary between two regions of the space-time. Such solutions are a generalized kind of spherically symmetric empty space solutions, described by metric functions of the class $C^0$. New global structures arise with surprising features. In particular, we show that…
Anomalies in Yang-Mills type gauge theories of gravity are reviewed. Particular attention is paid to the relation between the Dirac spin, the axial current j_5 and the non-covariant gauge spin C. Using diagrammatic techniques, we show that only generalizations of the U(1)- Pontrjagin four--form F^ F= dC arise in the chiral anomaly, even when coupled to gravity. Implications for Ashtekar's canonical approach to quantum gravity are discussed.
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.
We investigate quasilocal tachyon condensation by using gravity/gauge duality. In order to cure the IR divergence due to a tachyon, we introduce two regularization schemes: AdS space and a d=10 Schwarzschild black hole in a cavity. These provide stable canonical ensembles and thus are good candidates for the endpoint of tachyon condensation. Introducing the Cardy-Verlinde formula, we establish the on-shell gravity/gauge duality. We propose that the stringy geometry resulting from the off-shell tachyon dynamics matches onto the off-shell AdS black hole, where "off-shell" means non-equilibrium c…
The relationship between on-shell tree level scattering amplitudes of open and closed strings, discovered some time ago by Kawai, Lewellen and Tye, is used at field theory level (at $O(α'^3)$) to establish a link between the general relativity and the non-abelian Yang-Mills effective actions. Insisting at the effective Lagrangian level that any tree $N$ point gravity on-shell scattering amplitude is directly factorisable into a sum of $N$ point left-right products of non-abelian Yang-Mills tree on-shell scattering amplitudes, non-trivial mappings of the effective general relativity operators i…
We construct the generator of hamiltonian gauge symmetries in a 2+1 dimensional massive theory of gravity, proposed recently, through a systematic off-shell algorithm. Using a field dependant map among gauge parameters we show that the symmetries obtained from this generator are on-shell equivalent to the Poincaré gauge symmetries. We also clarify certain subtle issues concerning the implementation of this map.
We argue that finite-region observables in quantum gravity are best approached in terms of boundary data on null hypersurfaces. This has far-reaching effects on the basic notions of classical and quantum mechanics, such as Hamiltonians and canonical conjugates. Such radical properties are not unexpected in finite-region quantum gravity. We are thus motivated to reformulate field theory in terms of null boundary data. As a starting point, we consider the on-shell action functional for classical field theory in finite null-bounded regions. Closed-form results are obtained for free scalars and fo…
We study the renormalization flow of Hilbert-Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the precedin…
Renormalization of Quantum Gravity with Lagrange Multiplier Fields
Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Department of Applied Mathematics, The University of Western Ontario（韦仕敦大学应用数学系）；Department of Mathematics and Computer Science, Algoma University（阿尔戈马大学数学与计算机科学系）
In a spacetime of dimension n, the dual graviton is characterised by a Young diagram with two columns, the first of length n-3 and the second of length one. In this paper we perform the off-shell dualisation relating the dual graviton to the double-dual graviton, displaying the precise off-shell field content and gauge invariances. We then show that one can further perform infinitely many off-shell dualities, reformulating linearised gravity in an infinite number of equivalent actions. The actions require supplementary mixed-symmetry fields which are contained within the generalised Kac-Moody …
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized m…
We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a useful guide for non-perturbative studies of gravity. The Feynman rules for Regge's simplicial lattice formulation of gravity are then discussed in detail in two dimensions. As an application, the two-dimensional conformal anomaly due to a $D$-component scalar field is explicitly computed in perturbation theory.
In this work, we explore asymptotically flat charged thin-shell wormholes of third order Lovelock gravity in higher dimensions, taking into account the cut-and-paste technique. Using the generalized junction conditions, we determine the energy-momentum tensor of these solutions on the shell, and explore the issue of the energy conditions and the amount of normal matter that supports these thin-shell wormholes. Our analysis shows that for negative second order and positive third-order Lovelock coefficients, there are thin-shell wormhole solutions that respect the weak energy condition. In this …
We present an on-shell graphical framework for superamplitudes in super Yang-Mills theory with arbitrary supersymmetry. Our diagrammatic procedure is derived through manipulations of the full N = 4 superamplitude and illustrated by a number of explicit examples.
We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics. The fake particle, or "fakeon", which mediates interactions without appearing among the incoming and outgoing states, can be introduced by means of a new diagrammatics. The renormalization coincides with the one of the parent Euclidean diagrammatics, while unitarity follows from spectral optical identities, which can be derived by means of algebraic operations. The classical limit of a theory of physical particles and fakeons is described by an ordinary Lagrangian plus H…
We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo to show that graviton tree amplitudes are well behaved under large complex deformations of the momenta of a pair of like-helicity gravitons. This shows that BCFW recursion relations for gravity amplitudes can be constructed using such shifts, providing an alternative proof to the recent one by Arkani-Hamed and Kaplan. By using auxiliary recursion relations the cancellations which are hidden when using covariant Feynman diagrams become manifest.
In any gravitational theory and in a wide class of background space-times, we argue that there exists a simple, yet profound, relation between the on-shell Euclidean gravitational action and the on-shell Euclidean action of probes. The probes can be, for instance, charged particles or branes. The relation is tightly related to the thermodynamic nature of gravity. We provide precise checks of the relation in several examples, which include both asymptotically flat and asymptotically AdS space-times, with particle, D-brane and M-brane probes. Perfect consistency is found in all cases, including …
We study a novel proposal for the origin of cosmological cold dark matter (CDM) which is rooted in the quantum nature of spacetime. In this model, off-shell modes of quantum fields can exist in asymptotic states as a result of spacetime nonlocality (expected in generic theories of quantum gravity), and play the role of CDM, which we dub off-shell dark matter (OfDM). However, their rate of production is suppressed by the scale of non-locality (e.g. Planck length). As a result, we show that OfDM is only produced in the first moments of big bang, and then effectively decouples (except through its…
