Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal

L.B. Drissi et al. / Nuclear Physics B 804 [PM] (2008) 307–341 323Fig. 9. A typical the toric web-diagram of X 4 with boundary conditions (ΛΠΣΥ ).Fig. 10. Toric web-diagram of the local elliptic curve using 2d partitions. External and internal momenta have beenexpressed in terms of 2d partitions.where the sum over {ϰ} stands for the collective sum over the 2d partitions ϰ = τ , υ, ω, ϕ, ρ, σ ,ε, χ, ι, κ, ψ, ς and where we have setA τυ T ωϕ T ρσ T = C ∅τυ TC ∅ωϕ TC ∅ρσ T,B ετ T χρ T ψς T = C ∅ετ TC ∅χρ TC ∅ψς T,andF υε T ιψ T κω T = C ∅υε TC ∅ιψ TC ∅κω T, (3.56)G ϕκ T χσ T ις T = C ∅ϕκ TC ∅χσ TC ∅ις T,H τυωϕρσεχικψς =∏ϰ=τ,υ,ω,ϕ,ρ,σ,ε,χ,ι,κ,ψ,ς(−e−t ) |ϰ| q κ(ϰ) ,(3.57)where κ(μ) is the second Casimir of the 2d partition μ (2.8). The factors C αβγ are given byEq. (2.4).