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Old folklore says that there is no nontrivial renormalization group fixed point with U (1) gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially infinitely many) novel types of field theories with U (1) gauge symmetry by gauging U (1) × U (1) global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a nontrivial renormalization group fixed point for the U (1) gauge coupling constant and it will be a nontrivial conformal field theory without the U (1) × U (1) global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the θ -parameter is accompanied. [ABSTRACT FROM AUTHOR]

We study a higher group analog of the Weyl symmetry in four-dimensional quantum field theories. A typical example is that the modified transformation of the 2-form background gauge field replaces the operator-valued Weyl anomaly associated with gauging the 0-form global symmetry. It is analogous to the 2-group global symmetry where the modified transformation of the 2-form background gauge field replaces the operator-valued chiral anomaly associated with gauging the 0-form symmetry. The physical origin of the higher group Weyl symmetry is that under the renormalization group flow, the conserved current mixes with the electromagnetic current that couples with the dynamical gauge field. We can express these effects in the local renormalization group equations in a unified manner. [ABSTRACT FROM AUTHOR]

We investigate the properties of quarks and gluons above the chiral phase transition temperature , using the renormalization group (RG) improved gauge action and the Wilson quark action with two degenerate quarks mainly on a lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a nontrivial center. This is in agreement with our lattice simulation of high temperature quantum chromodynamics (QCD). We further observe that the temporal propagator of massless quarks at extremely high temperature remarkably agrees with the temporal propagator of free quarks with the twisted boundary condition for , but differs from that with the trivial boundary condition. As we increase the mass of quarks , we find that the thermal ensemble continues to be dominated by the twisted gauge field configurations as long as and above that the trivial configurations come in. The transition is similar to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks. [ABSTRACT FROM AUTHOR]

Gauging extra matter is a common way to couple two CFTs discontinuously. We may consider gauging matter by strongly coupled gauge theories at criticality rather than by weakly coupled (asymptotic free) gauge theories. It often triggers relevant deformations and possibly leads to a nontrivial fixed point. In many examples such as the IR limit of SQCDs (and their variants), the relevant RG flow induced by this strong gauging makes the total central charge increase rather than decrease compared with the sum of the original decoupled CFTs. The dilaton effective field theory argument given by Komargodski and Schwimmer does not apply because strong gauging is not a simple deformation by operators in the original two decoupled CFTs and it may not be UV complete. When the added matter is vector-like, one may emulate strong gauging in a UV completed manner by decoupling of ghost matter. While the UV completed description makes the dilaton effective field theory argument possible, due to the nonunitarity, we cannot conclude the positivity of the central charge difference in accordance with the observations in various examples that show the contrary. [ABSTRACT FROM AUTHOR]

In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant quantum field theories in d = 2 space–time dimensions necessarily possess the enhanced conformal symmetry. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in d = 2 space–time dimensions enjoy the conformal property relies on the deep structure of the renormalization group. The outstanding question is whether this feature is specific to d = 2 space–time dimensions or it holds in higher dimensions, too. As of January 2014, our consensus is that there is no known example of scale invariant but non-conformal field theories in d = 4 space–time dimensions under the assumptions of (1) unitarity, (2) Poincaré invariance (causality), (3) discrete spectrum in scaling dimensions, (4) existence of scale current and (5) unbroken scale invariance in the vacuum. We have a perturbative proof of the enhancement of conformal invariance from scale invariance based on the higher dimensional analogue of Zamolodchikov’s c -theorem, but the non-perturbative proof is yet to come. As a reference we have tried to collect as many interesting examples of scale invariance in relativistic quantum field theories as possible in this article. We give a complementary holographic argument based on the energy-condition of the gravitational system and the space–time diffeomorphism in order to support the claim of the symmetry enhancement. We believe that the possible enhancement of conformal invariance from scale invariance reveals the sublime nature of the renormalization group and space–time with holography. This review is based on a lecture note on scale invariance vs conformal invariance, on which the author gave lectures at Taiwan Central University for the 5th Taiwan School on Strings and Fields. [ABSTRACT FROM AUTHOR]

We show that a "constructive derivation" of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence based on the quantum local renormalization group in large-N quantum field theories consistently provides the a - c holographic Weyl anomaly in d = 4 at the curvature squared order in the bulk action. The consistency of the construction further predicts the form of the metric beta function. [ABSTRACT FROM AUTHOR]

Abstract: We discuss Weyl anomaly and consistency conditions of local renormalization group in dimensional quantum field theories. We give a classification of the consistency conditions and ambiguities in most generality within the power-counting renormalization scheme. They provide many non-trivial constraints on possible forms of beta functions, anomalous dimensions and Weyl anomaly of general dimensional quantum field theories. We perform modest checks of our results in conformal perturbation theories, supersymmetric field theories and holographic computations. [Copyright &y& Elsevier]

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 nonrenormalization 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 holography in the weakly coupled gravity regime. [ABSTRACT FROM AUTHOR]

Abstract: Null energy condition plays a crucial role in holographic renormalization group flow, leading to the holographic c-theorem. Unfortunately, the null energy condition is quantum mechanically violated. Even the averaged version can be violated. We discuss how the anomalous violation of the null energy condition affects the holographic renormalization group flow in -dimensional bulk gravity. We show that despite the violation of the null energy condition, a suitably modified holographic c-function with a peculiar log correction is still monotonically decreasing in so far as we add the counterterm that removes a ghost mode of gravity. [Copyright &y& Elsevier]

Abstract: It is logically possible that the trace anomaly in four dimensions includes the Hirzebruch–Pontryagin density in CP-violating theories. Although the term vanishes at free conformal fixed points, we realize such a possibility in the holographic renormalization group and show that it is indeed possible. The Hirzebruch–Pontryagin term in the trace anomaly may serve as a barometer to understand how much CP is violated in conformal field theories. [Copyright &y& Elsevier]