Related papers: On the $\mathcal{N}$ = 4, d = 4 pure spinor measur…

For the integrable spin-s XXZ chain we express explicitly any given spin-$s$ form factor in terms of a sum over the scalar products of the spin-1/2 operators. Here they are given by the operator-valued matrix elements of the monodromy…

Using the recent results in the pure spinor formulation, we lay out a ground-work towards the full momentum space amplitudes of open superstrings at three-loop. After briefly reviewing the one-loop amplitude, we directly work out the…

The simplest minimal subtraction method for massive {\lambda}{\phi}4 scalar field theory is presented. We utilize the one-particle irreducible vertex parts framework to deal only with the primitive divergent ones that can be renormalized…

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under $SO(1,10)$ Lorentz group. We first construct a bosonic M(atrix) theory by…

Beginning with the planar limit of N=4 SYM theory, we study planar diagrams for field theory deformations of N=4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one loop…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a bounded normal right quaternionic linear operator on $\mathcal{H}$. In this paper, we prove that there exists a unique spectral measure $E$ in $\mathcal{H}$ such that…

The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent…

We construct the integrated vertex operator for the first massive states of open superstrings with $(mass)^2=1/\alpha'$ in the pure spinor formalism of the superstring theory. This vertex operator is expressed in terms of the ten…

Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently…

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is…

It is a commonplace that any theory can be written in any coordinates via tensor calculus. But it is claimed that spinors as such cannot be represented in coordinates in a curved space-time. What general covariance means for theories with…

We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually…

We consider four-dimensional, Riemannian, Ricci-flat metrics for which one or other of the self-dual or anti-self-dual Weyl tensors is type-D. Such metrics always have a valence-2 Killing spinor, and therefore a Hermitian structure and at…

This paper investigates the question of which smooth compact 4-manifolds admit Riemannian metrics that minimize the L2-norm of the curvature tensor. Metrics with this property are called OPTIMAL; Einstein metrics and scalar-flat…

We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and non-minimal formulations, and show that they are equivalent. This is achieved by first coupling…

Held has proposed a coordinate- and gauge-free integration procedure within the GHP formalism built around four functionally independent zero-weighted scalars constructed from the spin coefficients and the Riemann tensor components.…

We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an…

We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally…

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$…

Four-dimensional supersymmetric type II string theory vacua can be described elegantly in terms of pure spinors on the generalized tangent bundle T+T*. In this paper, we apply the same techniques to any ten-dimensional supersymmetric…