Related papers: Spinor-Vector Duality in Heterotic String Orbifold…
We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that…
A manifestly T-dual invariant formulation of bosonic string theory is discussed here. It can be obtained by making both the usual string compact coordinates and their duals explicitly appear, on the same footing, in the world-sheet action.…
Recently multiple families of spin chain models were found, which have a free fermionic spectrum,even though they are not solvable by a Jordan-Wigner transformation. Instead, the free fermions emerge as a result of a rather intricate…
In this paper, an extension of the classification of flipped SU(5) heterotic-string vacua from [1] with a variation of the SO(10) breaking $\alpha$ basis vector is presented. A statistical sampling in the space of $2^{45}$ flipped SU(5)…
We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an…
We present a free field realisation for the vertex operator algebra associated to the genus-two, class $\mathcal{S}$ superconformal field theory of type $\mathfrak{a}_1$. The free field realisation is in the style of recent work by the…
We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H…
We study the M(atrix) theory which describes the $E_8 \times E_8$ heterotic string compactified on $S^1$, or equivalently M-theory compactified on an orbifold $(S^1/\integer_2) \times S^1$, in the presence of a Wilson line. We formulate the…
We present doubler-free gauge-invariant lattice vector gauge action for some real representations of Wilson gauge fields on an octet of fermions. It is based on a geometric representation of the Dirac equation as an evolution equation on…
We demonstrate the existence of heterotic-string vacua that are free of massless exotic fields. The need to break the non-Abelian GUT symmetries in k=1 heterotic-string models by Wilson lines, while preserving the GUT embedding of the…
We consider a simple theory of N free fermions in d dimensions with O\left(N\right) or U\left(N\right) symmetry. The singlet sector of this theory is expected from holography to be dual to the notoriously complicated Vasiliev gravity. By…
It is proved that there exist a vector representation of Dirac's spinor field and in one sense it is equivalent to biquaternion (i.e. complexified quaternion) representation. This can be considered as a generalization of Cartan's idea of…
We construct bosonic and fermionic matrix-vector models which describe orbifolded string worldsheets at a limit in which the dimension of the vector space and the matrix order are taken to infinity. We evaluate tree-level one-loop or…
M-theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ has recently been proposed to yield, via quotients, ten-dimensional non-supersymmetric string theories. We revisit the construction that leads to the heterotic theories, finding a consistent…
It is shown how the old Cartan's conjecture on the fundamental role of the geometry of simple (or pure) spinors, as bilinearly underlying euclidean geometry, may be extended also to quantum mechanics of fermions (in first quantization),…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…
This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the…
It has been conjectured that spontaneous chiral symmetry breaking in strongly coupled vectorlike gauge theories falls into only three different classes, depending on the gauge group and the representations carried by the fermions. We test…
We construct a model of M-theory vacua using gauged S-duality and the Chan-Paton symmetries by introducing an infinite number of open string charges. In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged S-duality…
Fermi transport of spinors can be precisely understood in terms of 2-spinor geometry. By using a partly original, previously developed treatment of 2-spinors and classical fields, we describe the family of all transports, along a given…