Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories

Gracey, J.A.; Ryttov, Thomas A.; Shrock, Robert

doi:10.1103/physrevd.97.116018

Cited by 22 publications

(20 citation statements)

References 120 publications

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“…Higher order beta and gamma functions are in general scheme dependent; perturbative scheme-independent approaches to higher loops have been developed for some QCD-like anomalous dimensions (see e.g. [41,42]), but not for the F operators relevant here. On the other hand, as x F grows, the fixed point rapidly becomes weakly coupled and the perturbative estimate of Eq.…”

Section: Modelling Compositeness Via Gauge-gravity Duality a The Hypercolour Theorymentioning

confidence: 99%

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

Elander

Frigerio

Knecht

et al. 2021

J. High Energ. Phys.

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We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spectrum for the various composite bosonic states, and study its dependence on the scaling dimension of the symmetry-breaking operators, as well as on the number of flavours. The different regions with a light dilaton are critically surveyed. We carefully assess the domain of validity of the holographic approach, and compare it with lattice simulations and the Nambu-Jona-Lasinio model.

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Section: Modelling Compositeness Via Gauge-gravity Duality a The Hypercolour Theorymentioning

confidence: 99%

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

Elander

Frigerio

Knecht

et al. 2021

J. High Energ. Phys.

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show abstract

“…The 4D fermion bootstrap has been studied in [26] and the techniques developed in the work can be directly employed for this study. 24 The baryon operator has UV scaling dimension ∆ U V B = 9/2, while it receives significant corrections due to strong coupling, and its IR scaling dimension ∆ IR B could possibly be much lower, see [110] for a scheme-independent perturbative study on the anomalous dimensions of baryon operators. The magnitude of ∆ IR B will likely directly affect whether the numerical bootstrap can generate strong bounds towards a physical theory.…”

Section: Jhep03(2021)172mentioning

confidence: 99%

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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“…4 See [29] and [30] for a clarification about the sign convention and a factor of 2 discrepancy in the overall normalization, also relevant for [31]. 5 Although this is unlikely to have caused any trouble, we feel compelled to mention that the preliminary results presented by one of us (GF) at a few recent seminars used a different sign convention and incorrectly stated some of the results for the (3/2, 0) case.…”

Section: Applications To Partial Compositenessmentioning

confidence: 99%

Anomalous dimensions of potential top-partners

Franzosi

Ferretti

2019

SciPost Phys.

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We discuss anomalous dimensions of top-partner candidates in theories of Partial Compositeness. First, we revisit, confirm and extend the computation by DeGrand and Shamir of anomalous dimensions of fermionic trilinears. We present general results applicable to all matter representations and to composite operators of any allowed spin. We then ask the question of whether it is reasonable to expect some models to have composite operators of sufficiently large anomalous dimension to serve as top-partners. While this question can be answered conclusively only by lattice gauge theory, within perturbation theory we find that such values could well occur for some specific models. In the Appendix we collect a number of practical group theory results for fourth-order invariants of general interest in gauge theories with many irreducible representations of fermions.

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Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories

Cited by 22 publications

References 120 publications

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

Searching for gauge theories with the conformal bootstrap

Anomalous dimensions of potential top-partners

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