27/32

TL;DR

This paper demonstrates a universal linear relationship between the central charges of N=2 and N=1 SCFTs connected by a mass deformation, explaining observed ratios and suggesting new theory connections.

Contribution

It establishes a universal linear transformation linking central charges during N=2 to N=1 SCFT flows, with implications for large N theories and previously unconnected models.

Findings

Central charges relate by a universal linear transformation.

In the large N limit, the ratio of central charges is 27/32.

Provides physical explanation for observed central charge ratios.

Abstract

We show that when an N=2 SCFT flows to an N=1 SCFT via giving a mass to the adjoint chiral superfield in a vector multiplet with marginal coupling, the central charges a and c of the N=2 theory are related to those of the N=1 theory by a universal linear transformation. In the large N limit, this relationship implies that the central charges obey a_IR/a_UV=c_IR/c_UV=27/32. This gives a physical explanation to many examples of this number found in the literature, and also suggests the existence of a flow between some theories not previously thought to be connected.