Abstract
We present a prescription for using the a central charge to determine the flow of a strongly coupled supersymmetric theory from its weakly coupled dual. The approach is based on the equivalence of the scale-dependent a-parameter derived from the four-dilaton amplitude with the a-parameter determined from the Lagrange multiplier method with scale-dependent R-charges. We explicitly demonstrate this equivalence for massive free N=1 superfields and for weakly coupled SQCD.
Highlights
Renormalization group (RG) flow of quantum field theories (QFTs) is thought to be irreversible. This irreversibility is encompassed by the Zamalodchikov c-theorem, which states that one can define a monotonically decreasing parameter that interpolates between the central charges c [1] of two conformal theories related by an RG flow
We discussed the use of the a central charge as a method of determining the flow in a strongly coupled supersymmetric theory from its weakly coupled dual
Crucial to the approach is the equivalence of the scale-dependent a parameter determined from the fourdilaton amplitude with an IR cutoff, and the a parameter determined in the Lagrange multiplier method of Refs. [17,18] with “flowing” R-charges
Summary
Renormalization group (RG) flow of quantum field theories (QFTs) is thought to be irreversible. At the fixed points there already exist well known relations between the anomalous dimensions of fields, their R-charges (via the superconformal field theory), and the a and c parameters The latter relations e.g., take the form a 1⁄4 3TrR3 − TrR; c 1⁄4 9TrR3 − 5TrR; ð1:4Þ where here R denotes the charges of states contributing to the ’t Hooft anomalies (i.e., it would be R − 1 if the superfield has charge R). The starting point of our discussion will be to demonstrate this unexpected equivalence, for flows near fixed points in the Banks-Zaks limit This gives some physical meaning to the Lagrange-multiplier method when the theory is strongly coupled. From there it is straightforward to determine the anomalous dimensions; the NSVZ beta function, and the gauge coupling in the strongly coupled description
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