Related papers: 4d N=2 SCFT and singularity theory Part III: Rigid…
This paper is a detailed study of a class of isolated Gorenstein threefold singularities, called hyperconifolds, that are finite quotients of the conifold. First, it is shown that hyperconifold singularities arise naturally in limits of…
To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian…
We study the $(1,0)$ six-dimensional SCFTs living on defects of non-geometric heterotic backgrounds (T-fects) preserving a $E_7\times E_8$ subgroup of $E_8\times E_8$. These configurations can be dualized explicitly to F-theory on elliptic…
We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form…
We study the $3d$ $\mathcal{N}=2$ theories resulting from the compactification of a family of $5d$ SCFTs on a torus with flux in the global symmetry. The family of $5d$ SCFTs used in the analysis is the one that UV completes the $5d$…
This paper is concerned with the analysis of a typical singularity of piecewise smooth vector fields on $R^3$ composed by two zones. In our object of study, the cusp-fold singularity, we consider the simultaneous occurrence of a cusp…
Supersymmetric and non-supersymmetric deformations of large $N=(4,4)$ SCFT with superconformal symmetry $D^1(2,1;\alpha)\times D^1(2,1;\alpha)$ are explored in the gravity dual described by a Chern-Simons $N=8$, $(SO(4)\times SO(4))\ltimes…
We employ a novel approach,based on homological mirror symmetry for Landau-Ginzburg models,to demonstrate the non-existence of crepant resolutions for certain weighted homogeneous Gorenstein compound Du Val singularities.Physically,this…
We prove that a general three-dimensional quartic $V$ in the complex projective space ${\mathbb P}^4$, the only singularity of which is a double point of rank 3, is a birationally rigid variety. Its group of birational self-maps is, up to…
We study Cox rings of crepant resolutions of quotient singularities $\mathbb{C}^3/G$ where $G$ is a finite subgroup of $SL(3,\mathbb{C})$. We use them to obtain information on the geometric structure of these resolutions, number of…
The Coulomb branch geometry of a 4d $\mathcal{N}=2$ SCFT is encoded in the data of a complex integrable system. In class-S, this is the Hitchin System (of ADE type) on the punctured curves $C$ on which we compactified from 6d to 4d. As we…
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of…
We study the four-dimensional N=2 superconformal field theories that describe D3-branes probing the recently constructed N=2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold…
We study 4D N=2 superconformal field theories that arise from the compactification of 6D N=(2,0) theories of type D_N on a Riemann surface, in the presence of punctures twisted by a Z_2 outer automorphism. Unlike the untwisted case, the…
In this work, we present a new geometric transition in non-compact Calabi-Yau 4-folds, specifically for the cone over the 7d Sasaki-Einstein manifold $Q^{\scriptscriptstyle(1,1,1)}/\mathbb{Z}_{N}$. We discover a new smoothing of such…
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…
Within the framework of four dimensional conformal supergravity we consider $\mathcal{N}=1,2,3,4$ supersymmetric theories generally twisted along the abelian subgroups of the R-symmetry and possibly other global symmetry groups. Upon…
We construct 4d $\mathcal{N}=1$ quantum field theories by compactifying the (2,0) theories on a Riemann surface with genus $g$ and $n$ punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative…
In this paper we set out to further explore the connection between isolated N=2 SCFT's in four dimensions and N=1 SCFT's in five dimensions. Using 5-brane webs we are able to provide IR Lagrangian descriptions in terms of 5d gauge theories…
We introduce a framework to prove integral rigidity results for the Seiberg-Witten invariants of a closed $4$-manifold $X$ containing a non-separating hypersurface $Y$ satisfying suitable (chain-level) Floer theoretic conditions. As a…