Large-Nc and Large-NF Limits of SU(Nc) Gauge Theories with Fermions in Different Representations

Sudhakantha Girmohanta*, Thomas A. Ryttov, Robert Shrock

*Corresponding author for this work

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Abstract

We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU(Nc) gauge theories with fermions transforming according to two different representations. We first study a theory with Nf fermions in the fundamental representation and Nf′ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc→∞, Nf→∞ with Nf/Nc fixed and finite. We then study the Nc→∞ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.

Original languageEnglish
Article number116022
JournalPhysical Review D
Volume99
Issue number11
Number of pages14
ISSN2470-0010
DOIs
Publication statusPublished - Jun 2019

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gauge theory
fermions
tensors
series expansion
operators

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title = "Large-Nc and Large-NF Limits of SU(Nc) Gauge Theories with Fermions in Different Representations",
abstract = "We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU(Nc) gauge theories with fermions transforming according to two different representations. We first study a theory with Nf fermions in the fundamental representation and Nf′ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc→∞, Nf→∞ with Nf/Nc fixed and finite. We then study the Nc→∞ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.",
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author = "Sudhakantha Girmohanta and Ryttov, {Thomas A.} and Robert Shrock",
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Large-Nc and Large-NF Limits of SU(Nc) Gauge Theories with Fermions in Different Representations. / Girmohanta, Sudhakantha; Ryttov, Thomas A.; Shrock, Robert.

In: Physical Review D, Vol. 99, No. 11, 116022, 06.2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Large-Nc and Large-NF Limits of SU(Nc) Gauge Theories with Fermions in Different Representations

AU - Girmohanta, Sudhakantha

AU - Ryttov, Thomas A.

AU - Shrock, Robert

N1 - 18 pages, RevTex

PY - 2019/6

Y1 - 2019/6

N2 - We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU(Nc) gauge theories with fermions transforming according to two different representations. We first study a theory with Nf fermions in the fundamental representation and Nf′ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc→∞, Nf→∞ with Nf/Nc fixed and finite. We then study the Nc→∞ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.

AB - We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU(Nc) gauge theories with fermions transforming according to two different representations. We first study a theory with Nf fermions in the fundamental representation and Nf′ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc→∞, Nf→∞ with Nf/Nc fixed and finite. We then study the Nc→∞ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.

KW - hep-th

KW - hep-lat

KW - hep-ph

U2 - 10.1103/PhysRevD.99.116022

DO - 10.1103/PhysRevD.99.116022

M3 - Journal article

VL - 99

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 11

M1 - 116022

ER -