We describe here the extension of the density matrix renormalization group algorithm to the case where Hamiltonian has a non-Abelian global symmetry group. The block states transform as irreducible representations of the non-Abelian group. Since the representations are multi-dimensional, a single block state in the new representation corresponds to multiple states of the original density matrix...

Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra FG for a large class of groups G. As an illustration of our methods, alternative constructions to some best linear codes over F2 and F3 are given. Furthermore, we give constructio...

Non–Abelian duality in relation to supersymmetry is examined. When the action of the isometry group on the complex structures is non–trivial, extended supersymmetry is realized non–locally after duality, using path ordered Wilson lines. Prototype examples considered in detail are, hyper–Kahler metrics with SO(3) isometry and supersymmetric WZW models. For the latter, the natural objects in the ...

We calculate the fundamental groups π = π1(P rB) for all irreducible plane sextics B ⊂ P2 with simple singularities for which π is known to admit a dihedral quotient D10. All groups found are shown to be finite, two of them being of large order: 960 and 21600.

Vortices carrying truly non-Abelian flux moduli, which do not dynamically reduce to Abelian vortices, are found in the context of softly-broken N = 2 supersymmetric chromodynamics (SQCD). By tuning the bare quark masses appropriately we identify the vacuum in which the underlying SU(N) gauge group is partially broken to SU(n)×SU(r)×U(1)/ZK , where K is the least common multiple of (n, r), and w...

We consider N = 1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(N c) and N c + N quark flavors. N c flavors are mass-less; the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with N c + N flavors...

We study the classical theory of a non-Abelian gauge field (gauge group SU(2)) coupled to a massive dilaton, massive axion and Einstein gravity. The theory is inspired by the bosonic part of the low-energy heterotic string action for a general Yang-Mills field, which we consider to leading order after compactification to (3 + 1) dimensions. We impose the condition that spacetime be static and s...

We present a wide class of reflexive, precompact, non-compact, Abelian topological groupsG determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group G are finite. We also show that many (non-reflexive) precompact Abelian ...

The topology assumed by most authors for a spacelike hypersurface in a spacetime containing a monopole is generally R3−{0}; save for the surface S2 isolating the monopole, this space is unbounded. For such a topology, a consistency relation of de Rham’s theorems shows that a single isolated monopole cannot exist. Monopoles, with charge ±m, if they exist at all, must occur in pairs having opposi...

Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G\Z(G) as the vertices of ΓG and join two distinct vertices x and y, whenever xy = yx. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finit...