%% Gives back beta-functions and anomalous dimensions, %% given combinatorial factors S, a1, and a2. function [betags,gamma_phi,gamma_phi2]=betas_gammas(d,gs,S,a1,a2,lambda1,lambda2) epsilon=6-d; %% Common factors I2=0; for X1=1:2 for X2=1:2 I2=I2+S(X1,X2)*gs(X1)*gs(X2); end end I4=0; for X1=1:2 for X2=1:2 for X3=1:2 for X4=1:2 for X5=1:2 I4=I4+S(X1,X5)*a1(X5,X2,X3,X4)*gs(X1)*gs(X2)*gs(X3)*gs(X4); end end end end end I3=zeros(2,1); for X=1:2 for X1=1:2 for X2=1:2 for X3=1:2 I3(X)=I3(X)+a1(X,X1,X2,X3)*gs(X1)*gs(X2)*gs(X3); end end end end I5A=zeros(2,1); for X=1:2 for X1=1:2 for X2=1:2 for X3=1:2 for X4=1:2 for X5=1:2 I5A(X)=I5A(X)+a2(X,X1,X2,X3,X4,X5)*gs(X1)*gs(X2)*gs(X3)*gs(X4)*gs(X5); end end end end end end I5B=zeros(2,1); for X=1:2 for X1=1:2 for X2=1:2 for X3=1:2 I5B(X)=I5B(X)+a1(X,X1,X2,X3)*gs(X1)*gs(X2)*I3(X3); end end end end %% Anomalous dimensions and beta functions % gamma_phi gamma_phi=(1/6)*I2+(-(11/216)+(1/3)*lambda1)*(I2^2)+((1/9)+(1/3)*lambda2)*I4; % gamma_phi2 gamma_phi2=I2+(-(1/24)+2*lambda1)*(I2^2)+(1+2*lambda2)*I4; % Beta functions % eta=gamma_phi; % nu=1/(2-eta+gamma_phi2) self_prop=(-epsilon/2); self_prop=self_prop+((1/4)+epsilon*lambda1)*I2; self_prop=self_prop+(-(11/144))*(I2^2); self_prop=self_prop+((1/6)+2*lambda1+(1/2)*lambda2)*I4; betags=self_prop*gs; betags=betags+(-1+epsilon*lambda2)*I3; betags=betags+((7/24)-2*lambda1-(1/2)*lambda2)*I2*I3; betags=betags-(1/2)*I5A; betags=betags+(-(3/4))*I5B; end