Renormalizations in abelian Chern-Simons field theories with matter

Avdeev, L.V.; Grigoryev, G.V.; Kazakov, D. I.

doi:10.1016/0550-3213(92)90659-y

Cited by 105 publications

(160 citation statements)

References 30 publications

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“…It is well known [14,15] that the gauge sector does not receive any UV correction. Moreover, a non-renormalization theorem for chiral integrals is still working in 3d and allows to conclude that the superpotential does not get infinite corrections.…”

Section: The Model and Its β-Functionsmentioning

confidence: 99%

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Infrared stability of ABJ-like theories

Bianchi

Penati

Siani

2010

J. High Energ. Phys.

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We consider marginal deformations of the superconformal ABJM/ABJ models which preserve N = 2 supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2) A × SU(2) B invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hepth].

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Section: The Model and Its β-Functionsmentioning

confidence: 99%

“…The theory can be quantized in a manifest N = 2 setup [14,16]. Perturbatively, UV divergences appear only at even orders in loops, so we concentrate on the renormalization of the theory at two loops.…”

Section: The Model and Its β-Functionsmentioning

confidence: 99%

Infrared stability of ABJ-like theories

Bianchi

Penati

Siani

2010

J. High Energ. Phys.

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“…In flat space, the renormalization of 2+1 dimensional quantum field theory has been studied at the perturbative level [12,13,14] and in the large N expansion [15,16,17,18,19]. Besides the finiteness of pure gravity in three dimensions [3], there have been studies on the renormalizability of quantum gravity near two dimensions [20].…”

Section: Introductionmentioning

confidence: 99%

Renormalization of quantum gravity coupled with matter in three dimensions

Anselmi

2004

Nuclear Physics B

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In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections, but are not sufficiently powerful to ensure finiteness. Therefore, it is necessary to perform an explicit (two-loop) computation in a specific model. I consider quantum gravity coupled with ChernSimons U (1) gauge theory and massless fermions and show that renormalization originates four-fermion divergent vertices at the second loop order. I conclude that quantum gravity coupled with matter, as it stands, is not finite in three spacetime dimensions.

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“…Firstly, there is the so called consistent dimensional regularization [9,10] in which ǫ µνλ is treated as essentially three dimensional, but one has to introduce a Maxwell or Yang-Mills kinetic term as a supplementary regularization. In another proposal, called dimensional reduction [6,[11][12][13]] the tensor algebra is done in three dimensions and afterwards the Feynman integrals are promoted to D dimensions. This method may introduce ambiguities in the finite parts of the amplitudes and also in the divergent parts in high order corrections.…”

Section: Introductionmentioning

confidence: 99%