Infrared Behaviour of SU(2) Gauge Theory with $N_f$ fundamental flavours

Leino, Viljami; Rummukainen, Kari; Suorsa, Joni M.; Tuominen, Kimmo; Tähtinen, Sara

doi:10.22323/1.336.0225

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…The chiral symmetry of SU(2) gauge theories coupled to fundamental massless fermions is enhanced from SU(N f ) × SU(N f ) to SU(2N f ) of which the fermion bilinears furnish a rank 2 representation. According to our previous result, a "fake" symmetry enhancement in the bootstrap bound of such fermion bilinears is expected as well, and the number of degrees of freedom of the fermion bilinears near/in the conformal window, such as N f = 6, 8 [85], is significantly larger than 18. The conclusion is that the kinks near N * are unlikely to be realized by SU(N c ) gauge theories coupled to fundamental fermions.…”

Section: Bounds Near the Critical Flavor Numbermentioning

confidence: 62%

“…There is strong evidence from lattice simulations that this . The anomalous mass dimension has also been computed using perturbative approaches: γ m ∼ 0.25 at four-loops [100,101], γ m ∼ 0.255 at five-loops [102], γ m ∼ 0.338 at fourth-order using scheme-independent series expansions [77,103], γ m ∼ 0.3375 − 0.352 using Padé resummations of these expansions [104], and γ ∼ 0.320 (85) in a recent work based on a Padé-Borel resummation of the coupling expansion [105].…”

Section: Bounds With N F = 12mentioning

confidence: 99%

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Searching for gauge theories with the conformal bootstrap

Poland

2021

J. High Energ. Phys.

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Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for SO(N) vector 4-point functions in general dimension D. In the large N limit, upper bounds on the scaling dimensions of the lowest SO(N) singlet and traceless symmetric scalars interpolate between two solutions at ∆ = D/2 − 1 and ∆ = D − 1 via generalized free field theory. In 3D the critical O(N) vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching ∆ = 1/2 at large N. We show that the bootstrap bounds also admit another infinite family of kinks $$ {\mathcal{T}}_D $$ T D , which at large N approach solutions containing free fermion bilinears at ∆ = D − 1 from below. The kinks $$ {\mathcal{T}}_D $$ T D appear in general dimensions with a D-dependent critical N* below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with SO(N) vectors, SU(N) fundamentals, and SU(N) × SU(N) bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of $$ {\mathcal{T}}_D $$ T D are subgroups of SO(N), and we speculate that the kinks $$ {\mathcal{T}}_D $$ T D relate to the fixed points of gauge theories coupled to fermions.

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Section: Bounds Near the Critical Flavor Numbermentioning

confidence: 62%

Section: Bounds With N F = 12mentioning

confidence: 99%

Searching for gauge theories with the conformal bootstrap

Poland

2021

J. High Energ. Phys.

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“…In the case of two colors, the location of the conformal window is more firmly established, as there is agreement among various groups that the model with n f ≥ 8 lies inside whereas the model with n f ≤ 4 lies outside [346,347,348,64,65,70,71,345]. The case n f = 6 is more debated and still not settled [346,349,350,351].…”

Section: Su(2) With Fundamental Fermionsmentioning

confidence: 99%

Fundamental Composite Dynamics: A Review

Cacciapaglia¹,

Pica²,

Sannino³

2020

Preprint

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We introduce fundamental gauge theories that can be employed to construct informed composite bright and dark extensions of the Standard Model, within and beyond the standard paradigms. The gap between theory and experiments is bridged by providing predictions and ways to test them, for example, at the Fermi scale and via precision flavor experiments. We will review time-honoured paradigms from (walking) technicolor to composite Goldstone Higgs and discuss their features and differences. Standard model fermion mass generation in composite models will also be discussed along with the challenges and opportunities that it offers. To be concrete and pedagogical we will concentrate on minimal constructions featuring strongly coupled gauge theories supporting the global symmetry breaking pattern SU(4)/Sp(4). The most minimal underlying fundamental description consists of an SU(2) gauge theory with two Dirac fermions transforming according to the fundamental representation of the gauge group. This minimal choice enables us to use first principle lattice results to predict the massive spectrum for models of composite (Goldstone) Higgs dynamics and strongly interacting dark matter, of immediate impact for current and future experimental searches. Because composite dynamics embraces a rich spectrum of theories with dynamics ranging from QCD-like behaviour to (near) conformal one, we also report here the state-of-the-art of numerical and analytic properties of several strongly coupled theories including their spectrum, phase diagrams and, when applicable, their (near) conformal data.

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“…Concerning the gauge group SU(2) with fundamental fermions, extensive investigations suggest no IRFP for N f = 2, 3, 4, while a IRFP is developed for N f = 6, 7, 8 [67,68]. For adjoint fermions, evidence for an IRFP have beem found for N F = 1, 3/2, 2 [69,70,71,72,73] and see [74,75] for recent developments.…”

Section: Conformal Window and Near-conformal β Functionsmentioning

confidence: 99%

Composite electroweak sectors on the lattice

Drach¹

2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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Infrared Behaviour of SU(2) Gauge Theory with $N_f$ fundamental flavours

Cited by 9 publications

References 17 publications

Searching for gauge theories with the conformal bootstrap

Searching for gauge theories with the conformal bootstrap

Fundamental Composite Dynamics: A Review

Composite electroweak sectors on the lattice

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