Related papers: Modular conjugation for multicomponent regions
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
In this paper, we construct the moduli spaces of filtered $G$-local systems on curves for an arbitrary reductive group $G$ over an algebraically closed field of characteristic zero. This provides an algebraic construction for the Betti…
We consider a Dirac field coupled minimally to the Mielke-Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological…
We present a detailed mass classification of all possible zero-energy modes in one-dimensional Dirac systems. By introducing a linear mass term into the Dirac Hamiltonian, we find that the topologically protected zero-energy modes have the…
In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\tau$-stability of Higgs pairs for…
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
Effects of fermion-vacuum polarization by a singular configuration of an external static vector field are considered in (2 + 1)-dimensional spacetime. Expressions for the induced vacuum charge and magnetic flux are obtained.
Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we…
In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory…
We introduce tropical singular intersection homologies (non-GM and GM) with the tropical coefficients on rational polyhedral spaces using their filtrations. We investigate their fundamental properties. In the non-GM case, we give a…
We work in the category $\mathcal{CLM}^u_k$ of [5] of separated complete bounded $k$-linearly topologized modules over a complete linearly topologized ring $k$ and discuss duality on certain exact subcategories. We study topological and…
The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another…
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamiltonian formulation with a canonical momentum field that is…
In this work, we provide evidence for a duality between 4-dimensional Calabi-Yau compactifications of the heterotic string, in which the base manifolds are linked by a conifold transition. In recent work, a geometric proposal was put…
We consider the dimensional reduction/compactification of supergravity, string and M-theories on tori with one time-like circle. We find the coset spaces in which the massless scalars take their values, and identify the discrete duality…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction…
We explore the moduli space of heterotic strings in two dimensions. In doing so, we introduce new lines of compactified theories with Spin(24) gauge symmetry and discuss compactifications with Wilson lines. The phase structure of d=2…
We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a…
Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…