Related papers: Sphere correlation functions and Verma modules
The effective field theory of heterotic vacua that realise $\mathbb{R}^{3,1}$ preserving $\mathcal{N} =1$ supersymmetry are studied. The vacua in question admit large radius limits taking the form $\mathbb{R}^{3,1}\times {X}$ , with ${X}$ a…
In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a…
We compute the supersymmetric partition function of $\mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $\mathcal{M}_4 \cong \mathcal{M}_{g,p}\times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$…
We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM…
The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable [Verrier P E and Evans N W 2008 J. Math. Phys. 49 022902] by finding an…
We revisit the factorisation of supersymmetric partition functions of 3d $\mathcal{N}=4$ gauge theories. The building blocks are hemisphere partition functions of a class of UV $\mathcal{N}=(2,2)$ boundary conditions that mimic the presence…
In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara n-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel…
We present a unified, ultraviolet-finite framework for the full Standard Model particle mass spectrum based on the Holomorphic Unified Field Theory augmented by nonlocal entire-function regulators. Starting from a single holomorphic action…
Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler…
We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To compensate for the dependence of this sum on perturbations,…
We study one of the simplest integrable two-dimensional quantum field theories with a boundary: $N$ free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an $(N-1)$-sphere of radius $1/\sqrt{g}$. The $N=1$…
We review some aspects of logarithmic conformal field theories which might shed some light on the geometrical meaning of logarithmic operators. We consider an approach, put forward by V. Knizhnik, where computation of correlation functions…
The Higgs branch of N=2 supersymmetric gauge theories with non-Abelian gauge groups are described by hyper-Kahler (HK) nonlinear sigma models with potential terms. With the non-Abelian HK quotient by U(M) and SU(M) gauge groups, we give the…
We study the space of vacua of three-dimensional $\mathcal{N}=4$ theories from a novel approach building on the type IIB brane realization of the theory and in which the insertion of local chiral operators in the path integral is obtained…
We formulate a conjectural relation between the category of line defects in topologically twisted 3d ${\cal N} = 4$ supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for…
Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also…
Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal…
Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of ${\cal N}=4$ super-Yang-Mills, the "hexagon program". This proposal results in several remarkable…
Starting with the projective-superspace off-shell formulation for four-dimensional N = 2 supersymmetric sigma-models on cotangent bundles of arbitrary Hermitian symmetric spaces, their on-shell description in terms of N = 1 chiral…
We describe a representation of the $q$--hypergeometric functions of one variable in terms of correlators of vertex operators made out of free scalar fields on the Riemann sphere.