Abstract. In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C ), spatial reflection (P) and time reversal (T ) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show tha...

It is well known that the lattice $${{\,\mathrm{Id_c}\,}}{G}$$ of all principal $$\ell $$ -ideals any Abelian -group G a completely normal distributive 0-lattice; yet not every 0-lattice homomorphic image some , via counterexample cardinality $$\aleph _2$$ . We prove with at most _1$$ elements By Stone duality, this means generalized spectral space compact open sets homeomorphic to subspace -sp...

Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They characterised, in particular, by the appearance a continuum conformal dimensions. Surprisingly, such CFTs have been identified as limits lattice models with finite number degrees freedom per site. However, results so far restricted case periodic boundary conditions, pre...

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...