Related papers: Notes on discrete torsion in orientifolds
We study string theory propagating on R^6 times K3 by constructing orientifolds of Type IIB string theory compactified on the T^4/Z_N orbifold limits of the K3 surface. This generalises the Z_2 case studied previously. The orientifold…
We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the…
We study discrete R-symmetries, which appear in 4D low energy effective field theory derived from hetetoric orbifold models. We derive the R-symmetries directly from geometrical symmetries of orbifolds. In particular, we obtain the…
Given a compact complex algebraic variety with an effective action of a finite group $G$, and a class $\alpha \in H^2(G,U(1))$, we introduce an orbifold elliptic genus with discrete torsion $\alpha$, denoted $Ell^{\alpha}_{orb}(X,G, q, y)$.…
We use the geometry of the space of fields for gauged supersymmetric mechanics to construct the twisted differential equivariant K-theory of a manifold with an action by a finite group.
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
By T-dualizing space-filling D-branes in IIB orientifold compactifications along the three non-internal spatial directions, we obtain black hole bound states living in a universe with a gauged spatial reflection symmetry. We call these…
The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of $\mathbf{q}$-CW complex structure on an orbifold, to detect torsion in its integral…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
The purpose of this paper is twofold: 1. we prove the triangulability of smooth orbifolds with corners, generalizing the same statement for orbifolds. 2. based on 1, we propose a new homology theory. We call it geometric homology theory…
This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point…
In this paper we study the analytic torsion and the $L^2$-torsion of compact locally symmetric manifolds. We consider the analytic torsion with respect to representations of the fundamental group which are obtained by restriction of…
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
We present special classes of orientifold models involving supersymmetry breaking via branes at angles. Type II superstring theories are compactified on a two torus times a four-dimensional orbifold. Combining worldsheet parity with a…
In this paper we construct an explicit geometric model for the group of gerbes over an orbifold $X$. We show how from its curvature we can obtain its characteristic class in $H^3(X)$ via Chern-Weil theory. For an arbitrary gerbe $\LL$, a…
In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem…
We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and…
We formulate the effective field theory of a D-particle on orbifolds of $T^4$ by a cyclic group as a gauge theory in a $V$-bundle over the dual orbifold. We argue that this theory admits Fayet-Iliopoulos terms analogous to those present in…
The discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts are investigated. We show that the discrete orthogonality relations hold for the case-(1)…
Using the algebraic geometry method of Berenstein and Leigh for the construction of the toroidal orbifold (T^2 x T^2 x T^2) / (Z_2 x Z_2) with discrete torsion and considering local K3 surfaces, we present non-commutative aspects of the…