Upper bound on the mass anomalous dimension in many-flavor gauge theories: A conformal bootstrap approach

Hisashi Iha, Hiroki Makino, Hiroshi Suzuki

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study four-dimensional conformal field theories with an SU(N) global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin 0 operator øki which belongs to the adjoint representation of SU(N). For N = 12 for example, we found that the theory contains a spin 0 SU(12)-breaking relevant operator when the scaling dimension of Øki, δ Øki, is smaller than 1.71. Considering the lattice simulation of many-flavor quantum chromodynamics with 12 flavors on the basis of the staggered fermion, the above SU(12)-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above SU(12)-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point γm ≤ 1.29 from the relation γm, = 3 - δ Øki, Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another SU(12)-breaking operator.

Original languageEnglish
Article number053B03
JournalProgress of Theoretical and Experimental Physics
Volume2016
Issue number5
DOIs
Publication statusPublished - May 2016

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gauge theory
operators
fermions
scaling
simulation
quantum chromodynamics
symmetry
curves

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Upper bound on the mass anomalous dimension in many-flavor gauge theories : A conformal bootstrap approach. / Iha, Hisashi; Makino, Hiroki; Suzuki, Hiroshi.

In: Progress of Theoretical and Experimental Physics, Vol. 2016, No. 5, 053B03, 05.2016.

Research output: Contribution to journalArticle

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abstract = "We study four-dimensional conformal field theories with an SU(N) global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin 0 operator {\o}ki which belongs to the adjoint representation of SU(N). For N = 12 for example, we found that the theory contains a spin 0 SU(12)-breaking relevant operator when the scaling dimension of {\O}ki, δ {\O}ki, is smaller than 1.71. Considering the lattice simulation of many-flavor quantum chromodynamics with 12 flavors on the basis of the staggered fermion, the above SU(12)-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above SU(12)-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point γ∗m ≤ 1.29 from the relation γ∗m, = 3 - δ {\O}ki, Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another SU(12)-breaking operator.",
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