I. Jack
We compute the one-loop beta-functions for renormalisable quantum gravity coupled to scalars using the co-ordinate space approach and generalised Schwinger De Witt technique. We resolve apparent contradictions with the corresponding momentum space calculations, and indicate how our results also resolve similar inconsistencies in the fermion case.
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We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of $SO(12),$ we show that the quantum field theory can be can be asymptotically free in all couplings (hence ultra-violet complete). For a region of parameter space, Dimensional Transmutation occurs, with the adjoint vacuum expectation value breaking $SO(12) \to SU(6)\otimes U(1)$ and producing a Low Energy Effective Theory having Einstein-Hilbert gravity. We verify that certain minima are locally stable and …
We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.
We calculate the three loop contribution to the beta-function of the gauge coupling constant in a general, anomaly-free, renormalisable gauge field theory involving a single gauge coupling using the background field method in the MSbar scheme.
We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of beta-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is ob…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yu…
Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this paper, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedman-Lemaitre-Robertson-Walker cosmological metric.
In this paper, we shall consider an infinite-derivative theory of gravity, with a view to making it renormalisable. First, we derive the modified superficial degree of divergence. Next, we establish that the theory is invariant under BRS (Becchi-Rouet-Stora) transformations. Consequently, we show that the corresponding Slavnov identities hold for the theory. Finally, we summarise our results and discuss renormalisability.
Renormalisation of postquantum-classical gravity
针对微扰量子引力不可重整化的问题，研究提出时空几何为经典、耦合量子物质的后量子经典引力理论，证明其形式可重整化且无快子与负模鬼场，给出完全正动力学证据并计算加速度功率谱，对相关研究与实验有重要意义。
We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that ν, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on ν, and for any positive νthere exist both a trivial and a nontrivial fixed point.
We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.
Quantum GraviElectro Dynamics
该研究提出了一种基于BRST量化的可重整化量子引力理论，即量子重力电动力学，展示了其在微扰下的可重整化性及引力耦合常数的实验测量方法。
General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions
本文给出了三维可重整化标量-费米子理论的一般四圈模板β函数和反常场维数，通过超对称性获得关系，并发现了一个在大N极限下受微扰控制的新非平凡红外不动点。
We recalculate the beta functions of higher derivative gravity in four dimensions using the one--loop approximation to an Exact Renormalization Group Equation. We reproduce the beta functions of the dimensionless couplings that were known in the literature but we find new terms for the beta functions of Newton's constant and of the cosmological constant. As a result, the theory appears to be asymptotically safe at a non--Gaussian Fixed Point, rather than perturbatively renormalizable and asymptotically free.
We explore the effect of quantum gravity on matter within a Renormalization Group framework. First, our results provide an explicit example of how misleading conclusions can be drawn by analyzing the gravitational contributions to beta functions, instead of analyzing universal quantities, such as critical exponents, that can be extracted from the beta functions. This could be key to explain differences between perturbative studies and Functional Renormalization Group studies. Second, we strengthen the evidence that asymptotically safe gravity could generate a predictive ultraviolet completion …
A symmetric zero mass tensor of rank two is constructed using the superstring modes of excitation which satisfies the physical state constraints of a superstring. These states have one to one correspondence with quantised operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensors using the Gupta-Bleuler method of quantisation. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantised field is deduced. The gravitational interaction is switched on by going over from…
An Observation on the Beta Functions in Quadratic Gravity
该研究针对二次曲率引力中的无量纲耦合beta函数展开，提出可通过简单论证限制任意圈阶抵消项推导的beta函数形式，并讨论了其与现有不同结果的关联。
We elucidate the connection between the N=1 beta-deformed SYM theory and noncommutativity. Our starting point is the T-duality generating transformation involved in constructing the gravity duals of both beta-deformed and noncommutative gauge theories. We show that the two methods can be identified provided that a particular submatrix of the O(3,3,R) group element employed in the former case, is interpreted as the noncommutativity parameter associated with the deformation of the transverse space. It is then explained how to construct the matrix in question, relying solely on information extrac…
Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory
本文在量子引力有效场论框架下，采用单引力子交换近似计算非阿贝尔规范理论中规范耦合常数的两圈贝塔函数，发现引力修正可能导致非平凡紫外固定点，其存在依赖于规范群与费米子数量。
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In par…
Based on considerations in conformal gauge I derive up to nextleading order a relation between the coefficients of beta-functions in 2D renormalizable field theories before and after coupling to gravity. The result implies a coupling constant dependence of the ratio of both beta-functions beyond leading order.
We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the sup…
We study a model in which p independent Ising spins are coupled to 2d quantum gravity (in the form of dynamical planar phi-cubed graphs). Consideration is given to the p tends to infinity limit in which the partition function becomes dominated by certain graphs; we identify most of these graphs. A truncated model is solved exactly providing information about the behaviour of the full model in the limit of small beta. Finally, we derive a bound for the critical value of the coupling constant, beta_c and examine the magnetization transition in the limit p tends to zero.
Matter Spectral Functions from Quantum Gravity
本文利用适用于洛伦兹号差的泛函重整化，研究渐近安全量子引力中引力涨落对光子和标量两点函数及谱表示的影响。
We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that non-renormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holo…
We obtain the correct all-loop beta-function of pure N=1 super Yang-Mills theory from the supergravity solution of the warped deformed conifold, including also some nonperturbative corrections. The crucial ingredient is the gauge-gravity relation that can be inferred by taking into account the phenomenon of gaugino condensation.
We study a gauge/gravity model for the thermodynamics of a gauge theory with one running coupling. The gravity side contains an ansatz for the metric and a scalar field, on the field theory side one starts by giving an ansatz for the beta function describing the scale dependence of the coupling. The model is based on relating the scale to the extra dimensional coordinate and the beta function to the gravity fields, thereby also determining the scalar field potential. We study three different forms of beta functions of increasing complexity and give semianalytic solutions describing first order…
We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful coupl…
We study the quantum properties of the three-dimensional higher derivative gravity. In particular we calculate the running of the gravitational and cosmological constants. The flow of these couplings shows that there exist both Gaussian and nontrivial fixed points in the theory, thus confirming that the theory is asymptotically safe. It is shown that the new massive gravity or $f(R)$ gravity in three dimensions do not correspond to the fixed point within the approximation that the coefficients of the higher curvature terms are not subject to the flow. The fixed point value of the cosmological …
In this work, we use the framework of effective field theory to couple Einstein's gravity to quantum electrodynamics (QED) and determine the gravitational corrections to the two-loop beta function of the electric charge in arbitrary electrodynamics (Lorentz-like) and arbitrary (de Donder like) gravitational gauges. Our results indicate that gravitational corrections do not alter the running behavior of the electric charge; on the contrary, we observe that it gives a positive contribution to the beta function, making the electric charge grow even faster.
We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the $λϕ^4$ and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are gauge dependent and, further, that they can be removed by a non-multiplicative, though local, field redefinition. An analogous analysis is carried out when General Relativity is replaced with Unimodular Gravity. Thus we show that a…
Beta functions of (3+1)-dimensional projectable Horava gravity
该研究推导了(3+1)维可投影Horava引力边际基本耦合的全套β函数，通过多步骤计算与规范验证，初步确定了候选渐近自由不动点，为该引力理论的重整化群分析提供关键结果。
Several calculations of 2- and 3-point correlation functions in the deformed theory are presented. The central charge in the Lunin-Maldacena gravity dual is shown to be independent of the deformation parameter. Calculations show that 2- and 3-point functions of chiral primary operators have no radiative corrections to lowest order in the interactions. Correlators of the operator tr(Z_1Z_2), which has not previously been identified as chiral primary, also have vanishing lowest order corrections.
We study extended objects in the gravity dual of the N=1 beta-deformation of N=4 Super Yang-Mills theory. We identify probe brane configurations corresponding to giant gravitons and Wilson loops. In particular we identify a new class of objects, given by D5-branes wrapped on a two-torus with a world-volume gauge field strength turned on along the torus. These appear when the deformation parameter assumes a rational value and the gauge theory spectrum has additional branches of vacua. We give an interpretation of the new D5-brane dual giant gravitons in terms of rotating vacuum expectation valu…
We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. Our result is consistent with the conjecture that Quantum Einstein Gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.
We discuss the ``gravitationally dressed'' beta functions in the Gross--Neveu model interacting with 2d Liouville theory and in $SU(N)$ gauge theory interacting with the conformal sector of 4d quantum gravity. Among the effects that we suggest may feel the gravitational dressing are the minimum of the effective potential and the running of the gauge coupling.
In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn't depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero …
The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut contributions needed to complete on-shell recursion relations for the integrand of scattering amplitudes in generic power-counting renormalisable theories at conjecturally any loop order. Our proposal meshes well with standard dimensional regularisation and applies in particular directly to much of the standard model of particle physics. Apart from a diagrammatic con…
We use gauge/gravity duality to study the thermodynamics of a generic almost conformal theory, specified by its beta function. Three different phases are identified, a high temperature phase of massless partons, an intermediate quasi-conformal phase and a low temperature confining phase. The limit of a theory with infrared fixed point, in which the coupling does not run to infinity, is also studied. The transitions between the phases are of first order or continuous, depending on the parameters of the beta function. The results presented follow from gauge/gravity duality; no specific boundary …
D-instantons are used to probe the near-horizon geometry of D3-branes systems on orbifold spaces. For fractional D3-branes, D-instanton calculus correctly reproduces the gauge beta-function and U(1)_R anomaly of the corresponding N=2 non-conformal Super Yang-Mills theories. For D3-branes wrapping the orbifold singularity, D-instantons can be identified with gauge instantons on ALE space, providing evidence of AdS/CFT duality for gauge theories on curved spaces.
We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group machine, for solving the flow equation, all the universal features of the one-loop beta-functions are recovered. While the universal part of the beta-functions admits two fixed points, we explicitly show that the existence of one of them depends on the choice of regularization scheme, indicating that it is most probably unphysical.
The standard argument why gravity is not renormalisable relies on direct powercounting of Feynman graphs to estimate the degree of UV divergence. This analysis has in several (highly) supersymmetric examples be shown to overestimate divergences considerably. In these examples the main improvements arise from a conjectured duality between color and kinematics. In this paper we initiate the systematic study of quite general powercounting under the assumption that color-kinematic duality exists. The main technical tool is a reformulation of the duality in terms of linear maps, modulo subtleties a…
We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations.Some of them are shown to be equivalent to the introduction of 2+$epsilon$-dimensional terms into the initially 2-dimensional theory. We also argue that the beta-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.
Physical running of couplings in quadratic gravity
本文指出二次引力的传统贝塔函数未能反映散射振幅对外部动量的真实依赖，重新推导出正确的物理贝塔函数，并证明渐近自由可与无快子条件相容。
We use gauge/gravity duality to study simultaneously the mass spectrum and the thermodynamics of a generic quasi-conformal gauge theory, specified by its beta function. The beta function of a quasi-conformal theory almost vanishes, and the coupling is almost constant between two widely separated energy scales. Depending on whether the gravity dual has a black hole or not, the mass spectrum is either a spectrum of quasinormal oscillations or a normal T=0 mass spectrum. The mass spectrum is quantitatively correlated with the thermal properties of the system. As the theory approaches conformality…
This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop …
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the `area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow po…
We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in $d=4$ spacetime dimensions. The fundamental role here is played by the ratio $x$ of the coupling in…
In this work we use the framework of effective field theory to couple Einstein's gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one graviton exchange. Studying the renormalization group functions we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational i…
We consider supergravity configuration of D5 branes wrapped on supersymmetric 2-cycles and use it to calculate one-point and two-point Green functions of some special operators in N=2 super Yang-Mills theory. We show that Green functions obtained from supergravity include two very different parts. One of them corresponds to perturbative results of quantum field theory, and another is a non-perturbative effect which corresponds to contribution from instantons with fractional charge. Comparing Green functions obtained from supergravity and gauge theory, we obtain radial/energy-scale relation for…
Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wave-function renormalization of the ghost fields. The latter induces non-trivial corrections to the beta-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point in agreement with the asymptotic safety conjecture, which also survives in the presence of extra dimensions. In four dimensions the g…
We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of gravity in the physical case of four dimensions.
We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $ϕ^2(iϕ)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\va…
We study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms we derive a system of beta functions for the running surface tension, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at $T\neq0$. Finally, we propose to identify the $D\rightarrow 0$ limit of the theory with two dimensional quantum gr…
We construct the one-loop effective action in Yang-Mills and Pure Quantum Gravity theories with heat kernel(or proper time method), which maintains manifest covariance during and after quantization (gauge and diffeomorphism invariance are always preserved). In this talk, we will basically focus on "What, How, and Why" we prefer heat kernel than the standard Feynman diagram calculation in momentum space at the one loop correction. The beta function of Yang-Mills field in the fixed gravitational background can be more simply obtained. The non-local term which cannot be easily obtained in the exp…
We make a systematic study of the cosmological dynamics for a number of f(R) gravity theories in Palatini formalism. We find a number of interesting results: (i) models based on theories of the type (a) f(R)=R-beta R^n and (b) f(R)=R+alpha ln R -beta, unlike the metric formalism, are capable of producing the sequence of radiation-dominated, matter-dominated and de-Sitter periods, and (ii) models based on theories of the type (c) f(R)=R+alpha R^m -beta R^n can produce early as well as late accelerating phases. However for the classes of models considered here, we have been unable to find the se…
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive g…
We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of…
Gauge dependence of momentum running in higher-derivative gravity
本文研究了高导数引力中曲率平方算子的一阶环动量运行的规范依赖性，发现其具有规范依赖性，并探讨了这一结果对理论物理可预测性的影响。
We construct a consistent closure for the beta functions of the cosmological and Newton's constants by evaluating the influence of the fluctuating metric and ghost fields anomalous dimensions on their flow. In this generalized framework we confirm the presence of a UV attractive non-Gaussian fixed-point. Our closure method is general and can be applied systematically to more general truncations of the gravitational effective average action.
The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet) are derived for the minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. The calculation is performed by means of the Barvinsky and Vilkovisky generalized Schwinger-DeWitt technique. With this result we gain, for the first time, the full set of the relevant beta functions in a super-renormalizable model of QG. The complete set of renormalization group (RG) equations, including also those for the Newton and the cosmological constant, is sol…
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