Abstract
We consider a non-Abelian gauge theory with Nf fermions and discuss the possible existence of a non-trivial UV fixed point at large Nf . Specifically, we study the anomalous dimension of the (rescaled) glueball operator Tr F2 to first order in 1/Nf by relating it to the derivative of the beta function at the fixed point. At the fixed point the anomalous dimension violates its unitarity bound and so the (rescaled) glueball operator is either decoupled or the fixed point does not exist. We also study the anomalous dimensions of the two spin-1/2 baryon operators to first order in 1/Nf for an SU(3) gauge theory with fundamental fermions and find them to be relatively small and well within their associated unitarity bounds.
Highlights
We find that while the anomalous dimensions of the baryon operators have small values at the fixed point, well consistent with the unitarity bound, the anomalous dimension of the glueball operator grows rapidly with increasing Nf grossly violating its unitarity bound
The beta function is known to leading order in 1/Nf and here we have extended these results to determine the anomalous dimensions of the glueball and spin-1/2 baryon operators to this same order
We evaluated the values of these anomalous dimensions at the UV fixed point
Summary
We consider a fermionic gauge theory with gauge group G and Nf number of Dirac fermions in some representation r of G. Most recently the five loop coefficient of the beta function has been computed in the MS scheme [24, 25] which represents the highest loop calculation for non-Abelian gauge theories. These coefficients generally depend on various (higher order) group invariants, the Riemann zeta function ζs and rational numbers. I ≥ 1 are polynomials in Nf. The first coefficient b1 is a polynomial in Nf to O(Nf ) while all the remaining coefficients bi, i ≥ 2 are polynomials in Nf to order O(Nfi−1). We find that the beta function can instead be written as β(A)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
