Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (or the number of corresponding left chiral anti-quark superfields). This implies that the number of left chiral quark superfields is half the number of quark flavours.

I've become a little reliant on the above relation to explain why beta functions are sometimes written differently for the same theory. For example I use it to explain the equivelance between equation \begin{align*} b_0 = 3N_C - N_f \end{align*} in Notes on Seibergology page 117 and equation \begin{align*} b_0 = 3N_C - (1/2)N_f \end{align*} in Supersymmetry and Beyond page 3 (where in the latter $C_2 (G)$ has been substituted for $N_C$). Both these equations are supposed to describe $N=1$, $SU(N_C)$ SQCD beta functions but they look different. The reason for this, I decided, was that in the first equation we're using $N_f$ as the number of left chiral quark superfields whilst in the latter equation $N_f$ corresponds to $n_f$ in the first paragraph of this question. In other words $N_f$ in the second equation actually means the number of flavours. Substituting $n_f$ in place of $N_f$ in the second equation then using $n_f = 2N_f$ shows that these two equations are actually the same.

This seemed to tie things up. However, Duality in Supersymmetric Yang-Mills Theory page 17 has the equation \begin{align*} b_0 = 3N_C - N_f \end{align*} where it explains on page 15 that $Nf$ is the number of flavours of quarks (we should substitute $N_f$ for $n_f$ using the notation established in the first paragraph of this question). It also explains on this page that we're indeed working with $N=1$, $SU(N_C)$ SQCD. So this seems to mess things up. Has the last paper just forgotten to divide by two and explained $N_f$ in an incorrect manner or am I missing something fundamental? I realise it's most likely the latter.

share|improve this question
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.