N=1 theories of class S_k
By D. Gaiotto, Shlomo S. Razamat. 2015
138 citations recorded by the source corpus.
We construct classes of ${\cal N}=1$ superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two integers (N,k). The k=1 case coincides with A_{N-1} ${\cal N}=2$ theories of class S and simple examples of theories with k>1 are Z_k orbifolds of some of the A_{N-1} class S theories. For the space of ${\cal N}=1$ theories to be complete in an appropriate sense we find it necessary to conjecture existence of new ${\cal N}=1$ strongly coupled SCFTs. These SCFTs when coupled to additional matter can be related by dualities to gauge theories. We discuss in detail the A_1 case with k=2 using the supersymmetric index as our analysis tool. The index of theories in classes with k>1 can be constructed using eigenfunctions of elliptic quantum mechanical models generalizing the Ruijsenaars-Schneider integrable model. When the elliptic curve of the model degenerates these eigenfunctions become polynomials with coefficients being algebraic expressions in fugacities, generalizing the Macdonald polynomials with rational coefficients appearing when k=1.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2f4793615a142ec4a25f35a5782bd9dde718727c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2 (2015, background): “Examples of this type have been studied recently in [76, 77], and at the level of holography in [78–80].”