### 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 ø^{k}_{i} 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 Ø^{k}_{i}, δ Ø^{k}_{i}, 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 Ø^{k}_{i}, 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 language | English |
---|---|

Article number | 053B03 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2016 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2016 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2016*(5), [053B03]. https://doi.org/10.1093/ptep/ptw046

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

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2016, no. 5, 053B03. https://doi.org/10.1093/ptep/ptw046

}

TY - JOUR

T1 - Upper bound on the mass anomalous dimension in many-flavor gauge theories

T2 - A conformal bootstrap approach

AU - Iha, Hisashi

AU - Makino, Hiroki

AU - Suzuki, Hiroshi

PY - 2016/5

Y1 - 2016/5

N2 - 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 γ∗m ≤ 1.29 from the relation γ∗m, = 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.

AB - 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 γ∗m ≤ 1.29 from the relation γ∗m, = 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.

UR - http://www.scopus.com/inward/record.url?scp=84997402753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84997402753&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptw046

DO - 10.1093/ptep/ptw046

M3 - Article

AN - SCOPUS:84997402753

VL - 2016

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 5

M1 - 053B03

ER -