(* This is an auxiliary Mathematica file accompanying the paper "A Flow in the Forest" by Alexander Gorsky, Vladimir Kazakov, Fedor Levkovich-Maslyuk, Victor Mishnyakov *)

(* We give the results for the correlators (1/N)<Tr ϕ> and (1/N)<Tr ϕ^3> discussed in section 4.2 of the paper *)

Result for Tr (ϕ^3)

Trϕ3=(1/(420 (π^2)))(105 (c^5) (((-1+p))^2) (π^2) (y^4) (2+3 (1+p) (y^2))-336 (c^5) M (y^2) (135+60 (1+p) (y^2)+(8+7 p+8 (p^2)) (y^4)) ((EllipticE[1-p])^2)+2 (c^(9/2)) π (Sqrt[c (y^2)]) (16 p (y^4) (21+4 (y^2)+4 (p^2) (y^2)+p (21-2 (y^2)))-63 M (60+45 (y^2)+9 (p^2) (y^2) (5+4 (y^2))+p (60+70 (y^2)+36 (y^4)))) EllipticK[1-p]-336 (c^5) M p (y^2) (45+6 (1+p) (y^2)+5 p (y^4)) ((EllipticK[1-p])^2)+(c^(9/2)) EllipticE[1-p] (2 π (Sqrt[c (y^2)]) (63 M (120+80 (1+p) (y^2)+9 (3+2 p+3 (p^2)) (y^4))-16 (y^4) (42+8 (y^2)+8 (p^3) (y^2)+(p^2) (42-5 (y^2))-p (42+5 (y^2))))+672 (Sqrt[c]) M (y^2) (45+6 (y^2)+(p^2) (y^2) (6+7 (y^2))+p (45+54 (y^2)+7 (y^4))) EllipticK[1-p]));

Result for Trϕ

Trϕ=(1/(2 (π^2)))(c^3) y ((1/60) π (y^3) (15 (((1-p))^2) π-32 ((((1-p))^2)+p) y EllipticE[1-p]-16 (-1-p) p y EllipticK[1-p])+M (6 y (-3+(-1-p) (y^2)) ((EllipticE[1-p])^2)+9 (-1-p) π EllipticK[1-p]-6 p π (y^2) EllipticK[1-p]-6 p y ((EllipticK[1-p])^2)+3 EllipticE[1-p] (π (6-(-1-p) (y^2))-4 y (-1-p-(y^2)+(1-p) (y^2)) EllipticK[1-p])));