Abstract
We describe an infinite two-parameter subfamily of theories of class $$ \mathcal{S} $$ where dialing one of the parameters interpolates between Gaiotto’s T N theory and a theory of N 2 free hypermultiplets. After using the reduced superconformal index to study the operator content, we use these theories to construct new $$ \mathcal{N} $$ = 1 SCFTs and then examine the flows between them.
Highlights
We are living in a golden age of quantum field theories
In theories of class S, a reduced version of the superconformal index (SCI) was found in [6], and it is possible to use this to infer the existence of some Higgs branch operators which are difficult to see from duality alone, along with some of their quantum numbers
Where F is the fermion number, E is the conformal dimension, R is the charge under the Cartan subgroup of the SU(2)R symmetry, r is the charge under the U(1)r symmetry, and (j1, j2) are the charges under the SU(2)1 × SU(2)2 Lorentz group. p, q and r are fugacities which keep track of the quantum numbers for each state in the theory, and the trace is over states on S3 in the usual radial quantization
Summary
We are living in a golden age of quantum field theories. The diversity of theories available to study is astonishing, and due to the technological advances of recent years, many strongly coupled theories that had been considered intractable are able to be investigated. A great deal of progress has been made on compactifications of the (2, 0) theory to two and three dimensions, in the present work we will be most interested in the four-dimensional theories that come from compactifying on a (punctured) Riemann surface This compactification can be done in such a way as to preserve N = 2 SUSY in four dimensions [1], and the resulting theories are called theories of class S. In theories of class S, a reduced version of the SCI was found in [6], and it is possible to use this to infer the existence of some Higgs branch operators which are difficult to see from duality alone, along with some of their quantum numbers It is far from obvious from the fixtures-and-punctures approach, we can construct a huge variety of new N = 1 theories.
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