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We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables, but they do appear in physically important correlation functions such as (anomalous) Ward–Takahashi identities or Schwinger–Dyson equations. We develop some tools such as embedding space delta functions and effective action to examine conformal invariance of these local terms. [ABSTRACT FROM AUTHOR]

While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field theories with discrete dilatation spectrum, it is not the case in more general situations without these assumptions. We indeed show that almost all the globally conformal invariant differential equations in two dimensions are neither Virasoro invariant nor Weyl invariant. The only exceptions are the higher spin conservation laws, conformal Killing tensor equations and the Laplace equation of a conformal scalar. [ABSTRACT FROM AUTHOR]

In this paper, we solve the two-point function of the lowest dimensional scalar operator in the critical theory on dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the cross-cap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage. [ABSTRACT FROM AUTHOR]

We investigate a possibility of scale invariant but nonconformal supersymmetric field theories from a perturbative approach. The explicit existence of monotonically decreasing a-function that generates beta-functions as a gradient flow provides a strong obstruction for such a possibility at two-loop order. We comment on the "discovery" of scale invariant but nonconformal renormalization group trajectories via a "change of scheme" in (4-ϵ) dimension proposed in literatures. [ABSTRACT FROM AUTHOR]

We show that relativistic hydrodynamics in Minkowski space-time has intrinsic ambiguity in second-order viscosity parameters in the Landau-Lifshitz frame. This stems from the possibility of improvements of energy-momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly nonconformal hydrodynamic theories can be hiddenly conformal invariant. [ABSTRACT FROM AUTHOR]

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the ϵ-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimensions. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories. [ABSTRACT FROM AUTHOR]

We construct a gravity dual for scale invariant but non-conformal field theories with a cyclic renormalization group flow. A slight modification of our construction gives a gravity dual of discretely scale invariant field theories. The underlying gravitational theory breaks the null energy condition. [ABSTRACT FROM AUTHOR]

Abstract: The free Maxwell theory in dimensions provides a physical example of a unitary, scale invariant theory which is NOT conformally invariant. The easiest way to see this is that the field strength operator is neither a primary nor a descendant. We show how conformal multiplets can be completed, and conformality restored, by adding new local operators to the theory. In , this can only be done by sacrificing unitarity of the extended Hilbert space. We analyze the full symmetry structure of the extended theory, which turns out to be related to the superalgebra. [Copyright &y& Elsevier]

Abstract: One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek–Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based on a vector condensation model coupled with the Euclidean Einstein–Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution. [ABSTRACT FROM AUTHOR]

The relation between scale invariance and conformal invariance is a subtle but important unsolved problem in the quantum field theory. We study a holographic approach to this problem and show that the null energy condition in the bulk effective gravitational theories guarantees the equivalence between the scale invariance and conformal invariance of the boundary theories. We also investigate the higher-dimensional compactification, where the warping can generate additional possible violation of the conformal invariance. Our discussion is applicable in any dimension, and suggests a generalization of Zamolodchikov-Polchinski theorem that states the equivalence in (1+1) dimension from the purely field theory viewpoint. [ABSTRACT FROM AUTHOR]