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Using a recently developed formulation of double field theory in superspace, the graviton, $B$-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as…

This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…

Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…

We analyze the relation between a topological coset model based on super $SL(2,R)/U(1)$ coset and non-critical string theory by using free field realization. We show that the twisted $N=2$ algebra of the coset model can be naturally…

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…

Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…

Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational…

We continue our investigation of the Kontsevich--Penner model, which describes intersection theory on moduli spaces both for open and closed curves. In particular, we show how Buryak's residue formula, which connects two generating…

We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such…

A careful gauge fixing of the conformal killing group (CKG) on genus zero surfaces in bosonic string theory gives non-vanishing two point amplitudes that match the corresponding field theory expressions arXiv:1906.06051, arXiv:1909.03672 .…

Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the…

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was…

We present a numerical linear programming bootstrap to construct dual model scattering amplitudes. Dual models describe tree-level exchanges of higher spin resonances in theories like string theory and large $N$ gauge theories. Despite…

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of…

We generalise our previous formulation of gauge-invariant PT-symmetric field theories to include models with non-Abelian symmetries and discuss the extension to such models of the Englert-Brout-Higgs-Kibble mechanism for generating masses…

We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter number,…

In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we…

Building upon previous $2D$ studies, this research focuses on describing $3D$ tensor renormalisation group (RG) flows for lattice spin systems, such as the Ising model. We present a novel RG map, which operates on tensors with…

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic…