Related papers: Gauge theory and mirror symmetry
It is well-known that if we gauge a $\mathbb{Z}_n$ symmetry in two dimensions, a dual $\mathbb{Z}_n$ symmetry appears, such that re-gauging this dual $\mathbb{Z}_n$ symmetry leads back to the original theory. We describe how this can be…
The geometry of submanifolds is intimately related to the theory of functions and vector bundles. It has been of fundamental importance to find out how those two objects interact in many geometric and physical problems. A typical example of…
We describe mirror symmetry in N=2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane. We show that the topological symmetries of Calabi-Yau…
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…
We explain why on certain five-manifolds, topological 5d $\mathcal{N} = 2$ gauge theory of Haydys-Witten twist with gauge group $G$, is dual to that of Geyer-M\"{u}lsch twist with gauge group $^LG$, where $G$ is a real, compact Lie group…
Witten's Gauged Linear $\sigma$-Model (GLSM) unifies the Gromov-Witten theory and the Landau-Ginzburg theory, and provides a global perspective on mirror symmetry. In this article, we summarize a mathematically rigorous construction of the…
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes…
We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…
We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the…
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional…
In a traditional gauge theory, the matter fields \phi^a and the gauge fields A^c_\mu are fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the Riemannian geometry covariant…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…
We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with…
One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to…
We perform a topological-holomorphic twist of $\mathcal{N}=4$ supersymmetric gauge theory on a four-manifold of the form $M_4=\Sigma_1 \times \Sigma_2$ with Riemann surfaces $\Sigma_{1,2}$, and unravel the mathematical implications of its…
We study two-dimensional topological gauge theories with gauge group equal to the symmetric group $S_n$ and their string theory duals. The simplest such theory is the topological quantum field theory of principal $S_n$ fiber bundles. Its…
In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on…