Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

Osborn, H.

doi:10.1016/0550-3213(91)80030-p

Cited by 306 publications

(683 citation statements)

References 49 publications

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“…Evidence that the conjecture may hold in four dimensions was presented in [4] while candidate counterexamples [5][6][7] were shown to actually be CFTs in [8,9]. As in the two-dimensional case, there is a connection between RG-flow and properties of the Wess-Zumino action [10,11] (see also [12,13]), the a-theorem, [14,15], and the scale vs conformal invariance problem. The conjecture is known to hold under some additional assumptions, for example for any scale invariant theory which is obtained by weakly coupled renormalisation group (RG) flows [8,13].…”

Section: Jhep08(2014)027mentioning

confidence: 99%

“…In this paper we assume that the dilatation operator is diagonalizable and the Weyl transformation rules are given by (3.5). As discussed in [2] in general dilatations may not be diagonalizable and the most general local transformations that are consistent with the Wess-Zumino consistency condition may contain additional terms [11,13]. It would be interesting to extend our analysis to the general case.…”

Section: Generating Functionalmentioning

confidence: 99%

“…We note however that there may exist a more general solution of the Wess-Zumino consistency condition which involves adding additional terms in the transformation rules (3.5) and the action (3.13). One may analyze this question by expanding the general solution of the Wess-Zumino consistency condition in [11,13] around a fixed point that is a SFT and collecting all terms that are cubic in the sources. We leave such analysis for future work.…”

Section: Jhep08(2014)027mentioning

confidence: 99%

“…If W denotes the generating functional of connected correlators for the SFT with gauged scaling symmetry, then its Weyl transformation δ σ W can be expressed as a variation of the local Wess-Zumino action δ σ S WZ . In this paper we need to include operators of dimension two and four and such operators contribute to scaling anomalies [11,30].…”

Section: Generating Functionalmentioning

confidence: 99%

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Comments on scale and conformal invariance

Bzowski

Skenderis

2014

J. High Energ. Phys.

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There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in correlation functions of the trace of the stress-energy tensor in such theories. We find that 2-, 3-and 4-point functions have a non-trivial anomaly while connected higher point functions are non-anomalous. We pay special attention to semi-local contributions to correlators (terms with support on a set containing both coincident and separated points) and show that the anomalies in 3-and 4-point functions can be accounted for by such contributions. We discuss the implications of the our results for the question of scale versus conformal invariance.

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Section: Jhep08(2014)027mentioning

confidence: 99%

Section: Generating Functionalmentioning

confidence: 99%

Section: Jhep08(2014)027mentioning

confidence: 99%

Section: Generating Functionalmentioning

confidence: 99%

See 2 more Smart Citations

Comments on scale and conformal invariance

Bzowski

Skenderis

2014

J. High Energ. Phys.

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“…To avoid this subtlety, we will adopt a real space renormalization group scheme in the following. Another advantage of using a real space RG scheme is the easiness in implementing a local RG [10,11,19,20] by choosing the speed of coarse graining differently at different points in space.…”

Section: Jhep09(2016)044mentioning

confidence: 99%

Horizon as critical phenomenon

Lee

2016

J. High Energ. Phys.

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We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

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Quantum field theories coupled to supergravity

Große

2008

Fortschritte der Physik

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This article is devoted to the investigation of the interplay of supersymmetric Yang–Mills theories (SYM) and supergravity (SUGRA). The topic is studied from two points of view: Firstly from the point of view of AdS/CFT correspondence, which realises the coupling of four dimensional superconformal 𝒩 = 4 SYM theory and ten dimensional type IIB SUGRA in a holographic way. In order to arrive at theories that resemble quantum chromodynamics (QCD) more closely, fundamental fields are introduced using probe D7‐branes and non‐trivial background configuration are considered. In particular supergravity solutions that are only asymptotically anti‐de Sitter and break supersymmetry are used. This allows the description of spontaneous chiral symmetry breaking. The meson spectrum is calculated and the existence of an associated Goldstone mode is demonstrated. Moreover it is shown that highly radially excited mesons are not degenerate. Additionally instanton configurations on the D7‐branes are investigated, which lead to a holographic description of the dual field theory's Higgs branch. Finally a holographic description of heavy‐light mesons is developed, which are mesons consisting of quarks with a large mass difference, such that a treatment of B mesons can be achieved The second approach is the technique of so‐called space‐time dependent couplings (also known as “local couplings”), where coupling constants are promoted to external sources. This allows to explore the conformal anomaly of quantum field theories coupled to a classical gravity background. The technique is extended to the superfield description of 𝒩 = 1 supergravity, a complete basis for the anomaly is given and the consistency conditions that arise from a cohomological treatment are calculated. Possible implications for an extension of Zamolodchikov's c‐theorem to four dimensional supersymmetric quantum field theories are discussed.

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Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

Cited by 306 publications

References 49 publications

Comments on scale and conformal invariance

Comments on scale and conformal invariance

Horizon as critical phenomenon

Quantum field theories coupled to supergravity

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