International Journal of Modern Physics A

A residue-theoretic representation is given for massless matter fields in (quotients of) (weighted) Calabi-Yau complete intersection models and the corresponding chiral operators in Landau-Ginzburg orbifolds. The well-known polynomial deformations are thus generalized, and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic reinterpretation. Also, a direct correspondence with a BRST type analysis of constrained systems emerges naturally.

Rational Hopf algebras, i.e. certain quasitriangular weak quasi-Hopf algebras whose representations form a tortile modular C* category, are expected to describe the quantum symmetry of rational field theories. In this paper the essential structure (hidden by a large gauge freedom) of rational Hopf algebras is revealed. This allows one to construct examples of rational Hopf algebras starting only from the corresponding fusion ring. In particular we classify all solutions for fusion rules with not more than three sectors, as well as for the level 3 affine fusion rules.

We construct new realizations of the Virasoro algebra inspired by the Calogero model. The Virasoro algebra we find acts as a kind of spectrum-generating algebra of the Calogero model. Furthermore, we present the superextension of these results and introduce a class of higher spin extensions of the Virasoro algebra which are of the W_∞ type.

Although the methods of calculation of power corrections in QCD sum rules are well known, algebraic complexity rapidly grows with the increase of vacuum condensates’ dimensions. Currently, state-of-the-art calculations include dimension 7 and 8 condensates. I summarize and extend algorithms of such calculations. First, I present all the formulae necessary for application of the systematic classification of bilinear quark condensates proposed earlier, and extend this method to the case of gluon condensates. Then I apply these systematic procedures to expansions of bilinear and noncollinear quark and gluon condensates in local ones, and of noncollinear condensates in bilocal ones. The formulae obtained can be used for calculation of correlators involving non-local condensates, and for inventing consistent ansätze for these condensates. Finally, I summarize the methods of calculation of heavy and light quark currents’ correlators. This paper aims both to present new results on gluon and nonlocal condensates and to be a self-contained handbook of formulae necessary for calculation of power corrections in QCD sum rules.