# 4d N=2 SCFT and singularity theory Part III: Rigid singularity

@article{Chen20174dNS, title={4d N=2 SCFT and singularity theory Part III: Rigid singularity}, author={Bingyi Chen and Dan Xie and Stephen S.-T. Yau and Shing-Tung Yau and Huaiqing Zuo}, journal={arXiv: High Energy Physics - Theory}, year={2017} }

We classify three fold isolated quotient Gorenstein singularity $C^3/G$. These singularities are rigid, i.e. there is no non-trivial deformation, and we conjecture that they define 4d $\mathcal{N}=2$ SCFTs which do not have a Coulomb branch.

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## References

SHOWING 1-10 OF 30 REFERENCES

### 4d N=2 SCFT and singularity theory Part II: Complete intersection

- Mathematics
- 2016

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine…

### 4d N=2 SCFT from Complete Intersection Singularity

- Mathematics
- 2016

Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum,…

### 4d N = 2 SCFT and singularity theory Part I: Classification

- Mathematics
- 2015

This is the first of a series of papers in which we systematically use singularity theory to study four dimensional N = 2 superconformal field theories. Our main focus in this paper is to identify…

### The versal deformation of an isolated toric Gorenstein singularity

- Mathematics
- 1994

Given a lattice polytope Q ⊆ ℝn, we define an affine scheme that reflects the possibilities of splitting Q into a Minkowski sum. Denoting by Y the toric Gorenstein singularity induced by Q, we…

### Gorenstein Quotient Singularities in Dimension Three

- Mathematics
- 1993

Introduction Classification of finite subgroups of $SL(3,\mathbb C)$ The invariant polynomials and their relations of linear groups of $SL(3,\mathbb C)$ Gorenstein quotient singularities in dimension…

### New N = 2 dualities

- Mathematics
- 2016

We consider N = 2 superconformal field theory with following properties: a) Coulomb branch operators have fractional scaling dimensions, b) there are exact marginal deformations . The weakly coupled…

### Algebraic classification of rational CR structures on topological 5-sphere with transversal holomorphic S-1-action in C-4

- Mathematics
- 2002

Let X be a compact connected CR manifold in ℂN. X is called a rational CR manifold if its geometric genus pg(X) is equal to zero. In this paper we classify all rational CR structures on a topological…

### BPS Structure of Argyres-Douglas Superconformal Theories

- Mathematics, Physics
- 1999

We study geometric engineering of Argyres–Douglas superconformal theories realized by type IIB strings propagating in singular Calabi–Yau threefolds. We use this construction to count the degeneracy…

### Argyres-Douglas matter and N=2 dualities

- Mathematics
- 2017

We study S duality of four dimensional N=2 Argyres-Douglas (AD) theory engineered from 6d A_{N-1} (2,0) theory. We find a (p,q) sequence of SCFTs, here (p,q) is co-prime and class S theory defined on…