Related papers: Quasi-periodic paths and a string 2-group model fr…
The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…
Four-dimensional compactifications of string theory provide a controlled set of possible gauge representations accounting for BSM particles and dark sector components. In this review, constraints from perturbative Type II string…
In this paper, we consider an arbitrary irreducible unitary representation $(\pi_{\lambda},V_{\lambda})$ of a compact connected, simply connected semisimple Lie group $G$ with highest weight $\lambda$, and apply the idea of…
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural…
These notes have been prepared for the Workshop on "(Non)-existence of complex structures on $\mathbb{S}^6$", to be celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey about the smallest…
The aim of this work is the study of left-invariant magnetic fields on 2-step nilpotent Lie groups. While the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the…
We show how the pseudo-linear interactions for spin-2 particles can be straightforwardly extended to include multiple massive and massless fields without introducing ghosts. When massive spin-2 fields are included, these give simple…
A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various versions of this notion have already been explored; our goal…
It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli…
The slice-independent gauge-fixed superstring chiral measure in genus 2 derived in the earlier papers of this series for each spin structure is evaluated explicitly in terms of theta-constants. The slice-independence allows an arbitrary…
We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular…
I describe how superstring theory may violate spin-statistics in an experimentally observable manner. Reviewing the basics of superstring interactions and how to utilize these to produce a statistical phase, I then apply these ideas to two…
In cosmological backgrounds, there can be 'partially massless' higher spin fields which have fewer degrees of freedom than their massive partners. The equations for the partially massless spin-2 fields are usually taken to be the linearized…
We present a systematic organization of functions and operators on the fuzzy 2-sphere in terms of string modes, which are optimally localized in position and momentum space. This allows to separate the semi-classical and the deep quantum…
Let $LG$ be the loop group of a compact, connected Lie group $G$. We show that the tangent bundle of any proper Hamiltonian $LG$-space $\mathcal{M}$ has a natural completion $\overline{T}\mathcal{M}$ to a strongly symplectic…
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
Closed bosonic string theory on toroidal orbifolds is studied in a Lagrangian path integral formulation. It is shown that a level one twisted WZW action whose field value is restricted to Cartan subgroups of simply-laced Lie groups on a…
We study the smooth $2$-group structure arising in the presence of quantum field theory with one-form symmetry. We acquire $2$-group structures obtained by a central extension of the zero-form symmetry by the one-form symmetry. We determine…
The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each component compactified as a…
A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology…