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We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a symmetric rank-2 tensor representation $S$ and $N+4$ copies (flavors) of a conjugate fundamental representation $\bar F$, together with a vectorlike subsector with chiral fermions in higher-dimensional representation(s).
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The Casimir invariants C 2 ( R ) C_{2}(R) and T ( R ) T(R) are defined as ∑ a ∑ j 𝒟 R ( T a ) i j 𝒟 R ( T a ) j k = C 2 ( R ) δ i k \sum_{a}\sum_{j}{\cal D}_{R}(T_{a})_{ij}{\cal D}_{R}(T_{a})_{jk}=C_{2}(R)\delta_{ik} and ∑ i , j 𝒟 R ( T a ) i j 𝒟 R ( T b ) j i = T ( R ) δ a b \sum_{i,j}{\cal D}_{R}(T_{a})_{ij}{\cal D}_{R}(T_{b})_{ji}=T(R)\delta_{ab} , where R R is the representation, T a T_{a} are the generators of G G , and D R D_{R} is the matrix representation ( Darstellung
Cited in the paper.
The coefficient 2 2 multiplying N v N_{v} in Eq. ( 10
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The term ( 7 / 4 ) N f (7/4)N_{f} for non-self-conjugate fermions is the sum of a term ( 7 / 8 ) N f (7/8)N_{f} for the fermions and ( 7 / 8 ) N f (7/8)N_{f} for the antifermions; in the case of a self-conjugate, Majorana fermion, these are the same
Cited in the paper.
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