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Goldman, Hart; Mulligan, Michael

doi:10.1103/physrevd.94.065031

Cited by 4 publications

(5 citation statements)

References 34 publications

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“…The conformal window extends for all N above N * . Indications of non-zero value of N * have been seen in previous large-N Schwinger-Dyson Equation study [70] and in -expansion calculation [71]. In a previous lattice study [52] to determine N * , we found that it is likely for N * to lie somewhere between 4 and 6, with N = 8 showing strong evidences in the finite-size scaling of low-lying Dirac eigen values for being scale-invariant in the infrared, with mass-anomalous dimension γ m ≈ 0.4.…”

Section: Three-dimensional Parity-invariant Su(2) Theory and Its Symm...supporting

confidence: 52%

Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR

Karthik

2021

Preprint

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We study the changes in the short-distance quark structure of the Nambu-Goldstone boson when the long-distance symmetry-breaking scales are depleted controllably. We achieve this by studying the valence Parton Distribution Function (PDF) of pion in 2+1 dimensional two-color QCD, with the number N of massless quarks as the tunable parameter that slides the theory from being strongly broken for N = 0 to the conformal window for N > 4, where the theory is gapped by the fixed finite volume. We perform our study non-perturbatively using lattice simulations with N = 0, 2, 4, 8 flavors of nearly massless two-component Wilson-Dirac sea quarks and employ the leading-twist formalism (LaMET/SDF) to compute the PDF of pion at a fixed valence mass. We find that the relative variations in the first few PDF moments are only mild compared to the changes in decay constant, but the shape of the reconstructed x-dependent PDF itself dramatically changes from being broad in the scale-broken sector to being sharply peaked in the near-conformal region, best reflected in PDF shape observables such as the cumulants.

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Section: Three-dimensional Parity-invariant Su(2) Theory and Its Symm...supporting

confidence: 52%

Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR

Karthik

2021

Preprint

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“…The four-dimensional SU (N c ) gauge theory coupled to massless fermions becomes infra-red free and loses asymptotic freedom above a certain number of fermion flavors. In 4− dimensions, -expansion calculation suggests the infra-red free behavior develops into a non-trivial conformal [15,16]. Also, an earlier analysis using the Schwinger-Dyson equations [17] using 1/N -expansion in three dimensions, similar to the one for the Abelian theory [18], suggests that the theory is scale invariant if…”

Section: Introductionmentioning

confidence: 94%

“…In 4 − ϵ dimensions, ϵ-expansion calculation suggests the infra-red free behavior develops into a non-trivial conformal (IR) fixed point if N > 11N c [15,16]. Also, an earlier analysis using the Schwinger-Dyson equations [17] using 1=N-expansion in three dimensions, similar to the one for the Abelian theory [18], suggests that the theory is scale invariant if N > 256 3π 2…”

Section: Introductionmentioning

confidence: 99%

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Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD

Karthik

Narayanan

2018

Phys. Rev. D

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We present a numerical study of three-dimensional two-color QCD with N ¼ 0, 2, 4, 8 and 12 flavors of massless two-component fermions using parity-preserving improved Wilson-Dirac fermions. A finite volume analysis provides strong evidence for the presence of SpðNÞ symmetry-breaking bilinear condensate when N ≤ 2 and its absence for N ≥ 8. A weaker evidence for the bilinear condensate is shown for N ¼ 4. We estimate the critical number of flavors below which scale-invariance is broken by the bilinear condensate to be between N ¼ 4 and 6.

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“…A LO estimate appeared in ref. [87]. In light of our results for QED 3 , it would be worth studying how this estimate is modified at NLO.…”

Section: Jhep12(2017)054mentioning

confidence: 99%

Scaling dimensions in QED3 from the ϵ-expansion

Pietro

Stamou

2017

J. High Energ. Phys.

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Abstract:We study the fixed point that controls the IR dynamics of QED in d = 4 − 2 dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the -expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to d = 3 to estimate their value at the IR fixed point of QED 3 as function of the number of fermions N f . The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of N f , which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the -expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of N f .

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Stability ofSU(Nc)QCD3

Cited by 4 publications

References 34 publications

Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR

Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR

Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD

Scaling dimensions in QED3 from the ϵ-expansion

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