We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero external momenta. The orthogonal approximation is employed to obtain the critical indices $η_{L2}$, $ν_{L2}$, $η_{L4}$ and $ν_{L4}$ diagramatically at least up to two-loop order in the anisotropic criticalities. This approximation is also utilized to compute the exponents $η_{L4}$ and $ν_{L4}$ in the isotropic case. Furthermore, we compute those exponents exactly for the isotropic behaviors at the same loop order. The results obtained for all exponents are in perfect agreement with those previously derived in the massless theories renormalized at nonzero external momenta.
We discuss the systematics of obtaining the Callan-Symanzik equation within the framework of the gauge/gravity dualities. We present a completely general formula which in particular takes into account the new holographic renormalization results of arXiv:1102.2239. Non-trivial beta functions are obtained from new logarithmic terms in the radial expansion of the fields. The appearance of multi-trace counterterms is also discussed in detail and we show that mixing between single- and multi-trace operators leads to very specific non-linearities in the Callan-Symanzik equation. Additionally, we com…
The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the $β$-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving …
We present an explicit analytical computation of the quantum corrections, at next-to-leading order, to the critical exponents. We employ for that the Unconventional minimal subtraction, recently proposed, and the Callan-Symanzik methods to probe the universality hypothesis by comparing the outcomes for the critical exponents evaluated in both methods and the ones calculated previously in massless theories renormalized at different renormalization schemes. Furthermore, the consistency of the former method is investigated for the first time in literature, to our knowledge. At the end, we compute…
Holography and Renormalization in Lorentzian Signature
De Boer et.等人发现了（d+1）维渐近反de Sitter空间中超引力的Hamilton-Jacobi方程与对偶d维扰动共形场论的Callan-Symanzik方程之间的渐近等价性。我们在洛伦兹签名中讨论这种对应。根据Marolf的构造方法，我们构造了初态和终态之间的关联函数的生成函数的引力对偶，并找到了一类结果具有经典超引力极限的态。我们展示了如何在场论中描述指定二阶超引力运动方程的全套解的数据，尽管运行耦合的重整化群方程具有一阶性质：必须指定耦合和状态，后者影响Callan-Symanzik方程的解。
On the link between finite QFT and standard RG approaches
Institute for Nuclear Research of the Russian Academy of Sciences（俄罗斯科学院核物理研究所）；Institute for Theoretical and Mathematical Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学理论与数学物理研究所）；Department of Particle Physics and Cosmology, Physics Faculty, M.V. Lomonosov Moscow State University（莫斯科国立大学物理学院粒子物理与宇宙学系）；Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（杜布纳联合核研究所鲍戈留博夫理论物理实验室）
We investigate spectral functions of matter-gauge theories that are asymptotically free in the ultraviolet and display a Banks-Zaks conformal fixed point in the infrared. Using perturbation theory, Callan-Symanzik resummations, and UV-IR connecting renormalisation group trajectories, we analytically determine the gluon, quark, and ghost propagators in the entire complex momentum plane. At weak coupling, we find that a Källén-Lehmann spectral representation of propagators is achieved for all fields, and determine suitable ranges for gauge-fixing parameters. At strong coupling, a proliferation o…
The infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory has been at the center of an intense debate over the last decade. Different solutions of the Dyson-Schwinger equations show a different behavior of the propagators in the infrared: in the so-called scaling solutions both propagators follow a power law, while in the decoupling solutions the gluon propagator shows a massive behavior. The latest lattice results favor the decoupling solutions. In this contribution, after giving a brief overview of the present status of analytical and semi-analytical approaches t…
We present analytical results for the Euclidean 2-point correlator of the flavor-singlet vector current evolved by the gradient flow at next-to-leading order ($O(g^2)$) in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormali…
