Analogs of the c-theorem for four-dimensional renormalisable field theories

Jack, I.; Osborn, H.

doi:10.1016/0550-3213(90)90584-z

Cited by 296 publications

(529 citation statements)

References 36 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%

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%

Comments on scale and conformal invariance

Bzowski

Skenderis

2014

J. High Energ. Phys.

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“…These models also obey the heuristic bound 11C(G) > 4 N ψ T (ψ) + N χ T (χ) proposed in [90,91] as well as the rigorous bounds from the a-theorem [92][93][94] …”

Section: Jhep06(2016)107mentioning

confidence: 99%

Gauge theories of partial compositeness: scenarios for Run-II of the LHC

Ferretti

2016

J. High Energ. Phys.

132

193

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We continue our investigation of gauge theories in which the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) and top-partners arise as bound states of three hyperfermions. All models have additional pNGBs in their spectrum that should be accessible at LHC. We analyze the patterns of symmetry breaking and present all relevant couplings of the pNGBs with the gauge fields. We discuss how vacuum misalignment and a mass for the pNGBs is generated by a loop-induced potential. Finally, we paint a very broad, qualitative, picture of the kind of experimental signatures these models give rise to, setting the stage for further analysis.

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“…In 2 dimensions this is established by Zamolodchikov c-theorem [2]. In 4 dimensions the monotonicity property of the anomaly coefficient a (a-theorem) was first conjectured in [3]; a perturbative proof was given by [4][5][6] with the local renormalization group (RG) equations. A proof using dispersion relations was given in [7,8].…”

Section: Introductionmentioning

confidence: 99%