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title: Gauge group constants
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permalink: /Gauge_group_constants/
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# Gauge group constants
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[Category:Calculations](/Category:Calculations "wikilink") SARAH supports not only chiral superfields in the fundamental representation but in any irreducible representation of *S**U*(*N*). In most cases, it is possible to fix the transformation properties of the chiral superfield by stating the corresponding dimension *D*. If the dimension is not unique, also the Dynkin labels are needed. For calculating kinetic terms and D-terms, it is necessary to derive from representation the corresponding generators. Furthermore, the eigenvalues *C*<sub>2</sub> of the quadratic Casimir for any irreducible representation *r*
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SARAH supports not only chiral superfields in the fundamental representation but in any irreducible representation of SU(N). In most cases, it is possible to fix the transformation properties of the chiral superfield by stating the corresponding dimension D. If the dimension is not unique, also the Dynkin labels are needed. For calculating kinetic terms and D-terms, it is necessary to derive from representation the corresponding generators. Furthermore, the eigenvalues C<sub>2</sub> of the quadratic Casimir for any irreducible representation r
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*T*<sup>*a*</sup>*T*<sup>*a*</sup>*ϕ*(*r*)=*C*<sub>2</sub>(*r*)*ϕ*(*r*)
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... | ... | @@ -25,7 +22,7 @@ are needed for the calculation of the RGEs. All of that is derived by SARAH due |
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*ρ* is the Weyl vector.
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5. The Dynkin index *I*(*r*) is calculated from *C*<sub>2</sub>(*r*). For this step, the value for the fundamental representation is normalized to $\\frac{1}{2}$.
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5. The Dynkin index *I*(*r*) is calculated from *C*<sub>2</sub>(*r*). For this step, the value for the fundamental representation is normalized to $`\frac{1}{2}`$.
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$I(r) = C_2(r) \\frac{D(r)}{D(G)}$
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With *D*(*G*) as dimension of the adjoint representation.
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