We discuss a new type of unitary perturbations around conformal theories inspired by the σ-model perturbation of the nonunitary WZNW model. We show that the nonunitary level k WZNW model perturbed by its sigma model term goes to the unitary level −k WZNW model. When plugged into the gauged WZNW model the given perturbation results in the perturbed gauged WZNW model which no longer describes a c...

Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are well-known in physics and play an important role in the theory of quantum error-correcting codes. Our algorithm is based on noncommutative Fourier analysis of co...

Higman has defined coset diagrams for PGL(2, ℤ). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in ℤ[𝔃], obtained by choosing a pair of words F[w i , w j ] such that both w i and w j fix a vertex v in γ. Two pairs of words are equivalent if an...

Example 1.1 (Cosets in R). Consider the vector space X = R. Let M be any onedimensional subspace of R, i.e., M is a line in R through the origin. A coset of M is a rigid translate of M by a vector in R. For concreteness, let us consider the case where M is the x1-axis in R , i.e., M = {(x1, 0) : x1 ∈ R}. Then given a vector y = (y1, y2) ∈ R , the coset y +M is the set y +M = {y +m : m ∈ M} = {(...

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2-th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 − 1 (respectively, 2), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs...

A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical ingredients of the latter –reduction of spacetime dimensions and the introduction of constraints– are examined. The consistency in the case of of group manifo...

1 The Setup {s:setup} The starting point is: a group G, a Cartan involution θ, and another involution σ of finite order, commuting with θ. It is natural to consider the coset σK = {σ ◦ int(k) | k ∈ K} ⊂ Aut(G). Every element of this coset commutes with θ. We’re mainly interested when σ is an involution, especially the case σ = θ. Now fix a pinning P = (H,B, {Xα}), and write δ, ǫ ∈ Aut(G) for th...

We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature. The bounds we obtain for locally correctable codes are worse than the best known bounds obtained using quantum information theory, but are better than those obtained using oth...

We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identi...

Electric-magnetic duality and higher dimensional analogues are obtained as symmetries in generalized coset constructions, similar to the axial-vector duality of twodimensional coset models described by Roček and Verlinde. We also study global aspects of duality between p-forms and (d−p−2)-forms in d-manifolds. In particular, the modular duality anomaly is governed by the Euler character as in f...