A sort of calculus is developed to find the chiral algebras of N=2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one or two generators, the number of relations is equal to the number of generators and they are algebraically independent.
Any four-dimensional $\mathcal{N} \geqslant 2$ superconformal field theory possess a protected subsector isomorphic to a two-dimensional chiral algebra \cite{Beem:2013sza}. The goal of these lectures is to provide an introduction to the subject, covering the construction of the chiral algebras, the consequences for four-dimensional physics, as well as a brief summary of recent progress. This is the writeup of the lectures given at the Winter School "YRISW 2020" to appear in a special issue of JPhysA.
We consider a family of $\mathcal{N}=2$ superconformal field theories in four dimensions, defined as $\mathbb{Z}_q$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $\mathcal{N}=1$ superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of $N$, exploiting the symmetries of the quiver to…
We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Rényi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $\math…
We show that four-dimensional superconformal algebras admit an infinite-dimensional derived enhancement after performing a holomorphic twist. The type of higher symmetry algebras we find are closely related to algebras studied by Faonte-Hennion-Kapranov, Hennion-Kapranov, and the second author with Gwilliam in the context of holomorphic QFT. We show that these algebras are related to the two-dimensional chiral algebras extracted from four-dimensional superconformal theories by Beem and collaborators; further deforming by a superconformal element induces the Koszul resolution of a plane in $\ma…
Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
对$\N=2,4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two, three and four point correlation functions. When $ \N =4 $, results are obtained for the three point function of various descendant operators, including the energy momentum tensor and SU(4) current. For both $ \N =2$导出了超共形变换，对手征准素算子的四点函数中出现的两个共形不变量的函数导出了4个超共形恒等式.这些都解决了一个单一的任意函数的两个共形不变量和一个或三个单变量函数。利用四维算子乘积展开中算子对标量四点函数的贡献的精确公式，将所得结果应用于算子乘积展开.给出了长超多重峰和可能的短超多重峰对手征准四点函数贡献的精确表达式。这些应用于给领导的微扰和大N修正的尺度尺寸的长超多重态。
We study $AdS_3 \times S^1 \times Y$ supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to ${\cal N}=2$ superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the ${\cal N}=2$ superconformal theory on $Y$.
We investigate superconformal quantum mechanics (SCQM) on a quantum computer. We study the ground state of the mass deformed SCQM on a quantum computed using the Variational Quantum Eigensolver (VQE) using a one boson and one boson - one fermion Hilbert space with and without noise and compare the accuracy of the results. We study the Feynman path integral for SCQM using the Evolution of Hamiltonian (EOH) algorithm on the quantum computer using the Trotter-Suzuki approximation and compare with the exact result. We consider an N boson and N fermion version of SCQM given be the Supersymmetric Ca…
We study the problem of constructing N=2 superconformal algebras out of an N=1 affine Lie algebra. Following a recent independent observation of Getzler and the author, we derive a simplified set of N=2 master equations, which we then proceed to solve for the case of sl(2). There is a unique construction for all noncritical values of the level, which can be identified as the Kazama-Suzuki coset associated to the hermitian symmetric space SO(3)/SO(2). We also identify the construction with a generalized parafermionic construction or, after bosonization, with a bosonic construction of the type a…
We study various orientifold projections of 4d $\mathcal{N}=1$ toric gauge theories, associated with CY singularities known as $L^{a,b,a}/\mathbb{Z}_2$, with $a+b$ even. We obtain superconformal chiral theories that have the same central charge, anomalies and superconformal index, whereas they were different before the orientifold. Some of these projections are implemented by a novel type of orientifold without fixed loci, known as glide orientifold. We claim that these theories flow to the same conformal manifold, and they are connected by quadratic exactly marginal deformations. The latter c…
