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This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…

We show that simultaneous gauge and supersymmetry breaking can be induced by radiative corrections, a la Coleman-Weinberg. When a certain correlation among the superpotential parameters is present, a local supersymmetry-breaking minimum is…

Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local…

An interesting framework to achieve gauge coupling unification consists in adding to the Standard Model Lagrangian non-renormalizable operators of $d \geq 5$, which affect the kinetic term of gauge fields. We first review the phenomenology…

This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number…

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical…

There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…

Mulmuley and Sohoni (GCT1 in SICOMP 2001, GCT2 in SICOMP 2008) proposed to view the permanent versus determinant problem as a specific orbit closure problem and to attack it by methods from geometric invariant and representation theory. We…

Hierarchical renormalization group (RG) transformations are related to nonassociative algebras. These algebras serve as a new basic tool for a rigorous treatment of global RG flows and the search of nontrivial infrared fixed points.…

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…

We demonstrate the utility of point group representation theory for symmetry analysis in resonant inelastic x-ray scattering. From its polarization-dependence, we show that a 5 eV inelastic feature in Sr2CuO2Cl2 has pure B1g symmetry and…

We study the principal sigma-models defined on any group manifold GL x GR/GD with breaking of GR, and their T-dual transforms. For abritary breaking we can express the torsion and Ricci tensor of the dual model in terms of the frame…

This paper is the second paper in a series of four papers that introduce cybersusy, which is a new method for analyzing supersymmetry breaking in the standard supersymmetric model (SSM). The first paper was a summary of the results and the…

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We…

Invoking increasingly higher dimension operators to encode novel UV physics in effective gauge and gravity theories traditionally means working with increasingly more finicky and difficult expressions. We demonstrate that local higher…

Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…

We establish an algorithm which computes formulae for the CR GJMS operators, the $P^\prime$-operator, and the $Q^\prime$-curvature in terms of CR tractors. When applied to torsion-free pseudo-Einstein contact forms, this algorithm both…

We aim to give a self-contained and detailed yet simplified account of the foundations of the theory of double operator integrals, in order to provide an accessible entry point to the theory. We make two new contributions to these…