discrete torsion
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2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Daniel G. Robbins ◽  
Eric Sharpe ◽  
Thomas Vandermeulen

Abstract This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.





Author(s):  
Christian Müller ◽  
Amir Vaxman

AbstractMotivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.



2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Simone Giacomelli ◽  
Mario Martone ◽  
Yuji Tachikawa ◽  
Gabi Zafrir

Abstract We carry out a systematic study of 4d $$ \mathcal{N} $$ N = 2 preserving S-folds of F-theory 7-branes and the worldvolume theories on D3-branes probing them. They consist of two infinite series of theories, which we denote following [1, 2] by $$ {\mathcal{S}}_{G,\mathrm{\ell}}^{(r)} $$ S G , ℓ r for ℓ = 2, 3, 4 and $$ {\mathcal{T}}_{G,\mathrm{\ell}}^{(r)} $$ T G , ℓ r for ℓ = 2, 3, 4, 5, 6. Their distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. We study various properties of these theories, using diverse field theoretical and string theoretical methods.



2021 ◽  
Author(s):  
Dongmin Jang ◽  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  


2020 ◽  
Vol 35 (24) ◽  
pp. 2050132
Author(s):  
Hervé Partouche ◽  
Balthazar de Vaulchier

The moduli space of the maximally supersymmetric heterotic string in [Formula: see text]-dimensional Minkowski space contains various components characterized by the rank of the gauge symmetries of the vacua they parametrize. We develop an approach for describing in a unified way continuous Wilson lines which parametrize a component of the moduli space, together with discrete deformations responsible for the switch from one component to the other. Applied to a component that contains vacua with [Formula: see text] gauge-symmetry factors, our approach yields a description of all backgrounds of the component in terms of free-orbifold models. The orbifold generators turn out to act symmetrically or asymmetrically on the internal space, with or without discrete torsion. Our derivations use extensively affine characters of [Formula: see text]. As a by-product, we find a peculiar orbifold description of the heterotic string in 10 dimensions, where all gauge degrees of freedom arise as twisted states, while the untwisted sector reduces to the gravitational degrees of freedom.



Author(s):  
Dongmin Jang ◽  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla


2018 ◽  
Vol 49 (5) ◽  
pp. 835-840
Author(s):  
E. I. Buchbinder
Keyword(s):  


2018 ◽  
Vol 61 (1) ◽  
pp. 121-150 ◽  
Author(s):  
Noé Bárcenas ◽  
Jesús Espinoza ◽  
Bernardo Uribe ◽  
Mario Velásquez

AbstractWe use a spectral sequence developed by Graeme Segal in order to understand the twisted G-equivariant K-theory for proper and discrete actions. We show that the second page of this spectral sequence is isomorphic to a version of Bredon cohomology with local coefficients in twisted representations. We furthermore explain some phenomena concerning the third differential of the spectral sequence, and recover known results when the twisting comes from finite order elements in discrete torsion.





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