Asymptotic safety with Majorana fermions and new large 
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 equivalences

Bond, Andrew D.; Litim, Daniel F.; Steudtner, Tom

doi:10.1103/physrevd.101.045006

Cited by 35 publications

(32 citation statements)

References 53 publications

(147 reference statements)

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“…15 A related issue is that there are many large N equivalences between different fixed points, e.g. [78]. Here ∆ * is the unitary bound for spin L operators (for instance, ∆ * = 1 for L = 0 in S sector), except for the T sector at L = 0, in which case ∆ * is given by ∆ T .…”

Section: Bootstrapping Fermion Bilinears In 4dmentioning

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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Section: Bootstrapping Fermion Bilinears In 4dmentioning

confidence: 99%

Searching for gauge theories with the conformal bootstrap

Poland

2021

J. High Energ. Phys.

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“…We will apply these expressions to compute RGEs for a scalar U(n) × U(n) matrix model, which has been of special interest e.g. due to the walking regime [66][67][68][69][70][71] between its two complex fixed points [72], as well as in models with weakly-coupled asymptotic safety in pertubatively exact settings [73][74][75][76][77] and extensions of the SM [78][79][80].…”

Section: Introductionmentioning

confidence: 99%

General scalar renormalisation group equations at three-loop order

Steudtner

2020

J. High Energ. Phys.

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For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

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“…In the following, we will demonstrate this observation for the case of gauge-Yukawa theories. These make for a particularly suitable example because (i) their fixedpoint structure is both rich enough and perturbatively wellcontrolled [34,36,38,39,42,73] and (ii) they are of direct phenomenological significance as possible extensions of the SM [37,40,41,43].…”

Section: Motivationmentioning

confidence: 99%

Effective Asymptotic Safety and Its Predictive Power: Gauge-Yukawa Theories

Held

2020

Front. Phys.

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Effective field theory provides a new perspective on the predictive power of Renormalization Group fixed points. Critical trajectories between different fixed points confine the regions of UV-complete, IR-complete, as well as conformal theories. The associated boundary surfaces cannot be crossed by the Renormalization Group flow of any effective field theory. We delineate cases in which the boundary surface acts as an infrared attractor for generic effective field theories. Gauge-Yukawa theories serve as an example that is both perturbative and of direct phenomenological interest. We identify additional matter fields such that all the observed coupling values of the Standard Model, apart from the Abelian hypercharge, lie within the conformal region. We define a quantitative measure of the predictivity of effective asymptotic safety and demonstrate phenomenological constraints for the associated beyond Standard-Model Yukawa couplings.

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Asymptotic safety with Majorana fermions and new large N equivalences

Cited by 35 publications

References 53 publications

Searching for gauge theories with the conformal bootstrap

Searching for gauge theories with the conformal bootstrap

General scalar renormalisation group equations at three-loop order

Effective Asymptotic Safety and Its Predictive Power: Gauge-Yukawa Theories

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