Related papers: Graded Geometric Structures Underlying F-Theory Re…
This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrically weighted graded modules of such modular forms, where the…
Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM)…
We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure with singularities on the diagonal of the square of the curve.
We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the…
We construct gauge theories with a vector-multiplet and hypermultiplets of $(1,0)$ supersymmetry on the six-sphere. The gauge coupling on the sphere depends on the polar angle. This has a natural explanation in terms of the tensor branch of…
We consider $1+1$ dimensional Yang-Mills theory with gauge group $G$ coupled to a massive Majorana fermion field in an adjoint representation and a number of massless Dirac or Majorana fermions transforming in arbitrary representations of…
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…
We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of the…
We present f(R) theories of ten-dimensional supergravities, including the fermionic sector up to the quadratic order in fermion fields. They are obtained by performing the conformal scaling on the usual supergravities to the f(R) frame in…
Moduli spaces of semi-stable real and quaternionic vector bundles of a fixed topological type admit a presentation as Lagrangian quotients, and can be embedded into the symplectic quotient corresponding to the moduli variety of semi-stable…
We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction…
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…
Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with…
In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally…
Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields $F_{\mu \nu}$. We derive a topological bound on ${\bf R}^8$, $\int_{M} ( F,F )^2 \geq k…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing…
The absence of fermion kinetic terms in supersymmetric-BF gauge theories is established. We do this by means of explicit off-shell (superspace) constructions. As part of our study we give the superspace constraints for D=3, N=4 super…