Congruence property in orbifold theory

RAMANUJAN'S FUNCTION r{n)—k CONGRUENCE PROPERTY

A Uniform Refinement Property for Congruence Lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt’s construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tůma. In a previous paper, we constructed a distributive algebraic lattice A with א2 compact elements that cannot be ob...

On a congruence property of elliptic curves

Let d, α ∈ Z with d > 1. In this paper, we proved the following results about congruence properties of elliptic curves: (1) For elliptic curve E over the rational number field Q, if ♯Ẽp(Fp) ≡ α (mod d) hold for almost all primes p, then almost all supersingular primes p of E satisfy p ≡ α − 1 (mod d). In particular, α−1 is prime to d. Moreover, if φ(d) > 2, then E does not have complex multipli...

New Duality Transformations in Orbifold Theory

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all currentalgebraic conformal field theories with a finite symmetry group H ⊂ Aut(g). The permutation orbifolds with H = Zλ and H = S3 are worked out in full as illustrations but the general formalism includes both simple and semisimple ...

High-energy effective theory for orbifold branes

Tetsuya Shiromizu, Shunsuke Fujii, Claudia de Rham and Hirotaka Yoshino Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan Advanced Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan and Ernest Rutherford Physics Building, McGill University, 3600 rue University, M...