Ian Balitsky
A Mellin-type representation of the graviton bulk-to-bulk propagator from Ref. 1 in terms of the integral over the product of bulk-to-boundary propagators is derived.
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We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.
We derive the graviton propagator on the brane for theories with quasi-localized gravity. In these models the ordinary 4D graviton is replaced by a resonance in the spectrum of massive Kaluza-Klein modes, which can decay into the extra dimension. We find that the effects of the extra polarization in the massive graviton propagator is exactly cancelled by the bending of the brane due to the matter sources, up to small corrections proportional to the width of the resonance. Thus at intermediate scales the classic predictions of Einstein's gravity are reproduced in these models to arbitrary preci…
The double-logarithmic four-graviton Regge sector as a rank-two twisted period system
研究N扩展超引力中的双对数四引力子Regge扇区，其Mellin空间解可表示为抛物线柱函数，并展示其作为二阶扭曲周期系统的结构，通过微分方程和递推关系统一描述超引力家族。
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can cons…
We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affect…
Graviton propagator in de Sitter space in a simple one-parameter gauge
本文研究了在德西特空间中使用一种简单一参数规范下的格拉维通传播子，该规范扩展了以往大多数德西特空间格拉维通环计算所使用的规范，所得传播子形式较为简单，有助于检验一阶计算中规范依赖性及所提观测量。
We formulate the graviton propagator on de Sitter background in a 2-parameter family of simple gauges which break de Sitter invariance. Explicit results are derived for the first order perturbations in each parameter. These results should be useful in computations to check for gauge dependence of graviton loop corrections.
We consider the covariant graviton propagator in de Sitter spacetime in a gauge with two parameters, alpha and beta, in the Euclidean approach. We give an explicit form of the propagator with a particular choice of beta but with arbitrary value of alpha. We confirm that two-point functions of local gauge-invariant quantities do not increase as the separation of the two points becomes large.
We consider the proposal of gr-qc/0508124 for the extraction of the graviton propagator from the spinfoam formalism. We propose a new ansatz for the boundary state, using which we can write the propagator as an integral over SU(2). The perturbative expansion in the Planck length can be recast into the saddle point expansion of this integral. We compute the leading order and recover the behavior expected from low-energy physics. In particular, we prove that the degenerate spinfoam configurations are suppressed.
We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum. We find an infinite number of poles with positive mass, but both positive and negative effective width, and studied their asymptotic behaviour in the infinite sheet Riemann surface. We find that the stability of these precursors depend crucially on the value of the normalisation point scale.
We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the propagators which reflect their gauge structure. This leads to a rapid determination of the physical part of the propagators in terms of elementary functions. The second method is a more traditional approach using covariant gauge fixing which leads to a solution for both physical and gauge parts of the propagators. The gauge invariant parts agree in both metho…
We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.
We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this prop…
We study the massive gravity theory proposed by Arkani-Hamed, Georgi and Schwartz. In this theory, the graviton becomes massive when general covariance is spontaneously broken through the introduction of a field that links two metrics, one of the which will eventually decouple. The excitation of this "link" field acts like a Goldstone boson in giving mass to the graviton. We work out the graviton and Goldstone boson propagators explicitly by means of gauge fixing terms similar to the renormalizability gauges used in gauge theories. With these propagators, we calculate the lowest order tree-lev…
We study the classical limit of the ELPR/FK spin foam models by analyzing the large-distance asymptotics of the corresponding graviton propagators. This is done by examining the large-spin asymptotics of the Hartle-Hawking wavefunction which is peaked around a classical flat spatial geometry. By using the stationary phase method we determine the wavefunction asymptotics. The obtained asymptotics does not give the desired large-distance asymptotics for the corresponding graviton propagator. However, we show that the ELPR/FK vertex amplitude can be redefined such that the corresponding Hartle-Ha…
The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors
研究四维量子引力在曲率展开至二次阶时，渐近安全形状因子驱动的背景引力子传播子流，构造零动量极限下的传播子并分析其动量依赖，发现仅有一个正留数的单极点，无鬼影极点，且牛顿势在原点正则。
We study the graviton propagator in euclidean loop quantum gravity, using the spinfoam formalism. We use boundary-amplitude and group-field-theory techniques, and compute one component of the propagator to first order, under a number of approximations, obtaining the correct spacetime dependence. In the large distance limit, the only term of the vertex amplitude that contributes is the exponential of the Regge action: the other terms, that have raised doubts on the physical viability of the model, are suppressed by the phase of the vacuum state, which is determined by the extrinsic geometry of …
A novel general expression is obtained for the graviton propagator from Lagrangian field theory by taking into account the necessary fact that in the functional differential approach of quantum field theory, in order to generate non-linearities in gravitation and interactions with matter, the external source $T_{μν}$, coupled to the gravitational field, should \textit{a priori} not be conserved $\partial^μT_{μν}\neq 0$, so variations with respect to its ten components may be varied \textit{independently}. The resulting propagator is the one which arises in the functional approach and does \tex…
A remarkably simple covariant graviton propagator in Anti-de Sitter spacetime
本文提出在任意维反德西特时空中，通过特殊规范选择得到极其简单的协变引力子和鬼传播子表达式，该规范改善了红外行为且平坦时空无法实现。
Simplicity of Mellin amplitudes for AdS$_3 \times$S$^3$
本文利用广义 Mellin 空间与在壳约束分扇区分解，给出 AdS$_3\ imes$S$^3$ 中半 BPS 标量初级算符全部四点树级关联子的简单 Mellin 振幅，并自举所有 KK 能级的引力子多重态关联子。
The pole truth: an analytical graviton propagator from Asymptotic Safety
从渐近安全推导出引力子传播子的解析近似，发现自旋-2扇区无额外极点且不违反幺正性与因果性，支持渐近安全不引入新自由度。
We describe closed string modes by open Wilson lines in noncommutative (NC) gauge theories on compact fuzzy G/H in IIB matrix model. In this construction the world sheet cut-off is related to the spacetime cut-off since the string bit of the symmetric traced Wilson line carries the minimum momentum on G/H. We show that the two point correlation functions of graviton type Wilson lines in 4 dimensional NC gauge theories behave as 1/(momentum)^2. This result suggests that graviton is localized on D3-brane, so we can naturally interpret D3-branes as our universe. Our result is not limited to D3-br…
We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity…
Graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are symmetry of the classical action, but do not leave path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such finite transformation the path integral measure changes and hence FFBRST transformation is capable of relating theories in two different gauges. We expli…
The one-loop unimodular graviton propagator in any dimension
使用维度正规化在任意时空维度下计算单模引力的完整单圈引力子传播子修正，基于 Weyl 不变性与 BRST 框架，并在 D=4 时获得重整化结果。
On-shell Bootstrap for n-gluons and gravitons scattering in (A)dS, Unitarity and Soft limit
提出基于三点振幅递归自举 (A)dS 中 n 点胶子和引力子振幅的算法，通过因子化及平直空间和软极限约束确定接触项，并映射到宇宙学关联函数，首次得到 AdS 中五引力子振幅。
In this paper we consider Witten diagrams at one loop in AdS space for scalar $ϕ^3+ϕ^4$ theory. After using Schwinger parametrization to trivialize the space-time loop integration, we extract the Mellin-Barnes representation for the one-loop corrections to the four-particle scattering up to an integration over the Schwinger parameters corresponding to the propagators of the internal particles running into the loop. We then discuss an approach to deal with those integrals.
Using on-shell amplitude methods, we explore 4-dimensional Electric-Magnetic duality and its double copy. We show explicitly that the on-shell scattering amplitudes know about `dual' photons (and dual gravitons), that the off-shell photon propagator double copies to the graviton propagator and that the magnetic part of the propagator is essential for the double copy to hold. We also show that there is an equivalent gravito-magnetic part of the graviton propagator which is essential in giving rise to solutions with either angular momentum or NUT charge. Furthermore, we comment on the so-called …
Theories with massive gravitons have peculiarity called the van Dam-Veltman-Zakharov discontinuity in that the massive theory propagator does not go to the massless graviton propagator in the zero graviton mass limit. This results in large deviation in Newtons law for massive graviton theories even when the graviton mass vanishes. We test the vDVZ in massive graviton theories for single graviton vertex process namely the gravitational radiation from a classical source. We calculate the gravitational radiation from compact binaries using the perturbative Feynman diagram method. We perform this …
Small mass graviton propagator via finite-field-dependent BRST transformations in the critical dimension Siegel-Zwiebach action from string theory
针对D=26中引力子传播子在无质量极限下的发散问题，通过有限场相关BRST变换连接不同的规范固定Siegel-Zwiebach生成泛函，在广义Lorenz型规范下实现了有限的连续极限传播子。
Black hole graviton and quantum gravity
基于思想实验提出动量超过普朗克尺度阈值的虚引力子会形成黑洞几何并使传播子为零，从而消除Feynman图贡献，为构建紫外有限的四维量子引力理论提供可行机制。
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.
Contributions of QED diagrams with vacuum polarization insertions to the lepton anomaly within the Mellin--Barnes representation
本文利用色散关系与Mellin-Barnes变换，首次给出四个同类型闭合轻子圈真空极化插入对轻子反常磁矩贡献的精确解析表达式，并分析了其渐近行为。
To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection. The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; …
We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also and a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplit…
In this work, we investigate the consequences of the spontaneous breaking of Lorentz symmetry, triggered by the bumblebee vector field, on the usual Einstein-Hilbert theory. Specifically, we consider the Einstein-Hilbert action modified by the bumblebee dynamic field, and evaluate the graviton propagator using an extended basis of Barnes-Rivers tensor projectors, involving the Lorentz-violating vector. Once the propagator is carried out, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity. We verify that this model po…
In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and …
From on-shell amplitude in AdS to cosmological correlators: gluons and gravitons
本研究补充了构建(A)dS时空中n点胶子与引力子Mellin动量振幅的递归自举方法的计算细节，阐释AdS在壳振幅定义动机并给出示例，同时展示了由该振幅推导宇宙学关联函数的方法。
Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats a…
We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been …
We point out some subtleties with gauge fixings (which sometimes include the so-called ``brane bending'' effects) typically used to compute the graviton propagator on the Randall-Sundrum brane. In particular, the brane, which has non-vanishing tension, explicitly breaks some part of the diffeomorphisms, so that there are subtleties arising in going to, say, the axial gauge or the harmonic gauge in the presence of (non-conformal) matter localized on the brane. We therefore compute the graviton propagator in the gauge where only the graviphoton fluctuations are set to zero (the diffeomorphisms n…
We address the issue of whether extra dimensions could have an infinite volume and yet reproduce the effects of observable four-dimensional gravity on a brane. There is no normalizable zero-mode graviton in this case, nevertheless correct Newton's law can be obtained by exchanging bulk gravitons. This can be interpreted as an exchange of a single {\it metastable} 4D graviton. Such theories have remarkable phenomenological signatures since the evolution of the Universe becomes high-dimensional at very large scales. Furthermore, the bulk supersymmetry in the infinite volume limit might be preser…
The proper spin-foam vertex amplitude is obtained from the EPRL vertex by projecting out all but a single gravitational sector, in order to achieve correct semi-classical behavior. In this paper we calculate the gravitational two-point function predicted by the proper spin-foam vertex to lowest order in the vertex expansion. We find the same answer as in the EPRL case in the `continuum spectrum' limit, so that the theory is consistent with the predictions of linearized gravity in the regime of small curvature. The method for calculating the two-point function is similar to that used in prior w…
We study non-planar correlators in ${\cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 \times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.
We obtain the full 5D graviton propagator in the Randall-Sundrum model with the Gauss-Bonnet interaction. From the decomposition of the graviton propagator on the brane, we show that localization of gravity arises in the presence of the Gauss-Bonnet term. We also obtain the metric perturbation for observers on the brane with considering the brane bending and compute the amplitude of one massless graviton exchange. For the positive definite amplitude or no ghost states, the sign of the Gauss-Bonnet coefficient should be negative in our convention, which is compatible with string amplitude compu…
We study the problem of semiclassical limit of Loop Quantum Gravity theory defined by the new spin foam models. This is done by analyzing the large-spin asymptotics of the Hartle-Hawking wavefunction. By using the stationary phase method we determine the wavefunction asymptotics, which then determines the large-distance asymptotics of the corresponding graviton propagator. We show that the graviton propagator behaves as the inverse distance to the fourth power. Our result is a direct consequence of the large-spin asymptotics of the spin foam model vertex amplitude, and it is valid for all new …
Mellin amplitudes for $AdS_3 \times S^3$
本文提出利用二维宇称奇共形块与四维宇称偶共形块的关系修正 Mellin 空间方法，并将其应用于 D1-D5 CFT，重现已知结果并得到引力子多重态四点相关函数的新紧凑公式。
The sixth order QED radiative corrections to lepton anomalies due to the fourth order vacuum polarization insertions within the Mellin-Barnes representation
本文利用色散关系和Mellin-Barnes变换，首次在全部质量比区间解析计算了含第四阶真空极化插入的第六阶QED轻子反常磁矩修正，并验证了渐近展开的精度与三类图的贡献区域。
In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS$_4$ via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the computation of a scalar factor. Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams also become relatively simple when written in momentum space. We explicitly calculate higher point correlators and discuss how this momentum space formalism makes flat space and collinear…
Hidden simplicity in AdS spinning Mellin amplitudes via scaffolding
通过scaffolding方法，研究AdS中旋进算子的Mellin幅度，发现其形式与平坦空间相似，且顶点比例系数简洁，体现正确极限。
We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions b…
In this thesis we mainly explore the evolution of both scalar and tensor cosmological perturbations in a Randall-Sundrum braneworld having an arbitrary expansion history. We adopt a four-dimensional perspective in which the localized degrees of freedom on the brane are regarded as an open quantum system coupled to the large environment composed of the Anti-de Sitter ($AdS$) bulk gravitons. Due to the non-uniform expansion of the universe, the brane degrees of freedom and the bulk degrees of freedom interact as they propagate forward in time, leading to an effective dissipation as well as a non…
Motivated by the interest raised by the problem of Lorenz-symmetry violating gauge theories in connetion with gravity models, this contribution sets out to provide a general method to systematically study the excitation spectrum of gravity actions which include a Lorentz-symmetry breaking Chern-Simons-type action term for the spin connection. A complete set of spin-type operators is found which accounts for the (Lorentz) violation parameter to all orders and graviton propagators are worked out in a number of different situations.
Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there is no systematic computational technique of the multiple series representations of $N$-fold MB integrals for $N>2$. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e logarithmic) and nonre…
We study the properties of the poles of the resummed graviton propagator obtained by resumming bubble matter diagrams which correct the classical graviton propagator. These poles have been previously interpreted as black holes precursors. Here, we show using the Horizon Wave-Function formalism that these poles indeed have properties which make them compatible with being black hole precursors. In particular, when modeled with a Breit-Wigner distribution, they have a well defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is …
We find explicitly the induced graviton propagator on de Sitter branes embedded in various five-dimensional spacetimes; de Sitter branes in AdS and Minkowski space are particular cases. By studying the structure of the momentum-space propagator, we are able to extract interesting physics, much of which is qualitatively different from that of flat branes. We find that 1) there can be a set of graviton-like particles which mediate brane gravity at different scales; 2) localized gravity can exist even on de Sitter branes in Minkowski space; 3) Kaluza-Klein modes also contribute to conventional 4-…
Gravitons are described by the propagator in Teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermo Field Dynamics formalism. The Gravitational Casimir effect and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.
Dirichlet gravitons in AdS$_4$ and $\mathcal{L}_Λw_{1+\infty}$ wedge algebra
本文从 AdS$_4$ 旋量-螺旋度表示出发，通过 Mellin 变换构造 Dirichlet 边界条件下的软引力子代数，唯一确定软模括号，得到 $\mathcal L_\Lambda w_{1+\infty}$ 楔形代数，为宇宙学常数形变提供了体推导。
A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $ξ$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($ξ= 0$) the graviton…
Despite the nice geometrical properties of higher dimensional Chern-Simons (CS) supergravity theories these actions suffer from one major drawback, namely, their connection with the real world. After some quick remarks on three-dimensional gravity, we consider five-dimensional CS supergravity and study to what extend this theory reproduces the standard low energy description of gravitons and gauge fields. We point out that if one deforms the CS action by changing the value of the cosmological constant by a small amount (thus breaking the CS symmetry), propagation around AdS becomes non-trivial…
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