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 the mini-versal deformation of these singularities, and therefore solve the Coulomb branch spectrum and Seiberg-Witten solution.

AaRSs (aminoacyl-tRNA synthetases) group into two ten-member classes throughout evolution, with unique active site architectures defining each class. Most are monomers or homodimers but, for no apparent reason, many bacterial GlyRSs are heterotetramers consisting of two catalytic α-subunits and two tRNA-binding β-subunits. The heterotetrameric GlyRS from Escherichia coli (EcGlyRS) was historically tested whether its α- and β-polypeptides, which are encoded by a single mRNA with a gap of three in-frame codons, are replaceable by a single chain. Here, an unprecedented X-shaped structure of EcGlyRS shows wide separation of the abutting chain termini seen in the coding sequences, suggesting strong pressure to avoid a single polypeptide format. The structure of the five-domain β-subunit is unique across all aaRSs in current databases, and structural analyses suggest these domains play different functions on α-subunit binding, ATP coordination and tRNA recognition. Moreover, the X-shaped architecture of EcGlyRS largely fits with a model for how two classes of tRNA synthetases arose, according to whether enzymes from opposite classes can simultaneously co-dock onto separate faces of the same tRNA acceptor stem. While heterotetrameric GlyRS remains the last structurally uncharacterized member of aaRSs, our study contributes to a better understanding of this ancient and essential enzyme family.

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 N = 2 SCFTs which do not have a Coulomb branch. 1(3) We can also turn on expectation value of operator E r,(0,0) : u r = E r,(0,0) .A central question of understanding 4d N = 2 SCFT is to understand the low energy physics for general deformations parameterized by S = (λ, m, u r ). The low energy physics is best captured by the Seiberg-Witten geometry [SW]. Usually Seiberg-Witten geometry is described by a family of Rieman surfaces fibered over space S, and it is conjectured in [XY] that more general Coulomb branch geometry can be captured by the miniversal deformation of certain kind of three fold singularity X [GLS]. Roughly speaking, a deformation is a flat morphism π : Y → S, with π −1 (0) isomorphic to the singularity X, and a mini-versal deformation essentially captures all the deformations. Here S is identified with the parameter space (λ, m, u r ) of our (generalized) Coulomb branch.Therefore the study of 4d N = 2 SCFT and its Coulomb branch solution are reduced to the study of singularity X and its mini-versal deformation. We have classified such X which can be described by complete intersection [XY, YY1, CX], and the physical aspects of these 4d N = 2 SCFTs are studied in [XY1, XY2, XY3, XYY]. All the complete intersection examples studied in [XY, YY1, CX] have non-trivial mini-versal deformation and therefore non-trivial Coulomb branch.The purpose of this note is to study non-complete intersection rational Gorenstein singularities. An interesting class of such singularities are quotient singularity C 3 /G with G a finite subgroup of SL(3). One of main results of this paper is the classification of the three dimensional isolated Gorenstein quotient singularity.We then would like to study mini-versal deformation of these singularities, and a surprising theorem by Schlessinger [S] shows that all such singularities are rigid, i.e. they have no non-trivial deformation 1 . Therefore the corresponding 4d theory has no Coulomb branch 2 . We call such theories rigid N = 2 theories. It would be very interesting to study more properties of these theories.2. Three-fold singularity and 4d N = 2 SCFT Let's discuss more about the interpretation of N = 2 SCFT defined using three fold rational Gorenstein singularity (they are also called canonical singularity [R]). There are two special ways of smoothing a singularity: crepant resolution [R] and mini-versal deformation [GLS]. For the singularities we are interested, we have following facts:1 See [V] for example of rigid compact Calabi-Yau manifolds. 2 Free hypermultiplets do have a Coulomb branch as we can turn on mass deformation.

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The polyketide natural product reveromycin A (RM-A) exhibits antifungal, anticancer, anti-bone metastasis, anti-periodontitis and anti-osteoporosis activities by selectively inhibiting eukaryotic cytoplasmic isoleucyl-tRNA synthetase (IleRS). Herein, a co-crystal structure suggests that the RM-A molecule occupies the substrate tRNAIle binding site of Saccharomyces cerevisiae IleRS (ScIleRS), by partially mimicking the binding of tRNAIle. RM-A binding is facilitated by the copurified intermediate product isoleucyl-adenylate (Ile-AMP). The binding assays confirm that RM-A competes with tRNAIle while binding synergistically with l-isoleucine or intermediate analogue Ile-AMS to the aminoacylation pocket of ScIleRS. This study highlights that the vast tRNA binding site of the Rossmann-fold catalytic domain of class I aminoacyl-tRNA synthetases could be targeted by a small molecule. This finding will inform future rational drug design.