We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Zp , whenever p is a fixed prime. For the induction step, we introduce the ...

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some norm...

We consider a BRST approach to G/H coset WZNW models, i.e. a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and ...

This study proposes a novel suboptimal embedding algorithm for binary messages based on a lowweight search embedding (LWSE) strategy. The suboptimal LWSE strategy involves using algorithm to perform an embedding procedure by using a parity check matrix. The optimal embedding algorithm, which is based on the maximun likelihood (ML) algorithm, aims to locate the coset leader and minimize embeddin...

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary Coset Conformal Field Theories, i.e., gauged Wess-ZuminoWitten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic Quantum Field Theory (QFT) to approach Coset Conformal Field Theories. Two main conjectures are formulated and their consequences are discu...

By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a special way to separate the dependence on the coset field. The coset field is then regard...

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-ZuminoWitten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences are discussed. Some ...

Fractional quantum Hall fluids with fillings 2 < ν < 3 have been recently proposed which generalize the Pfaffian state (ν = 2 + 1/2) into a hierarchy of states with parafermionic excitations. We describe here the corresponding Zk-parafermion conformal field theory by means of the coset construction ŝu(k)1⊕ ŝu(k)1/ŝu(k)2. This extends our earlier derivation of the Pfaffian state from a “parent” ...

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E10(R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility...

The spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is derived from the spinconnection. It is shown how the degeneracy of the lowest Landau level in the recently proposed higher dimensional quantum Hall effect i...