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Related papers: Folds in 2D String Theories

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Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

Soft Condensed Matter · Physics 2025-10-20 João C. Neves , Bernardo R. Marques , Cristóvão S. Dias , Nuno A. M. Araújo

A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…

Differential Geometry · Mathematics 2023-03-14 Jan Vysoky

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d N=1 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning…

High Energy Physics - Theory · Physics 2013-08-15 Sebastian Franco , Daniele Galloni , Rak-Kyeong Seong

We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a…

High Energy Physics - Theory · Physics 2014-11-18 Ivan K. Kostov , Matthias Staudacher

We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in hep-th/0504229.…

High Energy Physics - Theory · Physics 2008-11-26 Ofer Aharony , Justin R. David , Rajesh Gopakumar , Zohar Komargodski , Shlomo S. Razamat

Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the…

Mathematical Physics · Physics 2008-04-21 J. Manuel Garcia-Islas

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

Geometric Topology · Mathematics 2015-05-14 J. C. Gómez-Larrañaga , F. González-Acuña , Wolfgang Heil

Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small…

High Energy Physics - Theory · Physics 2009-10-22 Joseph A. Minahan

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…

High Energy Physics - Theory · Physics 2019-05-22 Arthur J. Parzygnat

We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by…

High Energy Physics - Theory · Physics 2009-11-07 M. Billo' , A. D'Adda , P. Provero

This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…

Algebraic Topology · Mathematics 2021-10-01 Naoki Kitazawa

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…

Human-Computer Interaction · Computer Science 2024-10-28 Marina Evers , Lars Linsen

These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…

High Energy Physics - Theory · Physics 2008-02-03 Boris Dubrovin

We study matrix quantum mechanics at a finite temperature equivalent to one dimensional compactified string theory with vortex (winding) excitations. It is explicitly demonstrated that the states transforming under non-trivial U(N)…

High Energy Physics - Theory · Physics 2015-06-25 Dmitri Boulatov , Vladimir Kazakov

Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face…

High Energy Physics - Theory · Physics 2015-06-12 Sebastian Franco

Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…

Geometric Topology · Mathematics 2022-08-16 Naoki Kitazawa

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…

High Energy Physics - Theory · Physics 2011-09-13 Taro Kimura

Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…

High Energy Physics - Theory · Physics 2023-01-10 O. D. Andreev , R. R. Metsaev , A. A. Tseytlin

We introduce and initiate the investigation of a general class of 4d, N=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as…

High Energy Physics - Theory · Physics 2015-06-05 Sebastian Franco
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