We show that the conformal invariance conditions for a general σ-model with torsion are invariant under T -duality through two loops.

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface in a Lorentzian spacetime naturally inherits from the spacetime metric a diierentiation D e , the so-called real Sen connection, which turns out to be determined completely by the initial data h ab and ab induced on , and coincides, in the case of vanishing second fundamenta...

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen’s σ-constant, also known as the smooth Yamabe number. We prove that if N is obtained from M by surgery of codimension at...

A bstract Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, a focus on duality invariant (2 n ? 1)-form chiral 2 -form in Minkowski spacetime dimension D = 4 + 2, respectively. We exhibit new family 2-form 6 for which these exhaust possibilities conformal invariance; limit is related by dimen...

We associate to a compact spin manifoldM a real-valued invariant τ(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen’s σ-constant, also known as the smooth Yamabe number. We prove that if N is obtained fromM by surgery of codimension at...

We establish conditions under which the worldsheet β-functions of logarithmic conformal field theories can be derived as the gradient of some scalar function on the moduli space of running coupling constants. We derive a renormalization group invariant version of this function and relate it to the usual Zamolodchikov C-function expressed in terms of correlation functions of the worldsheet energ...

We consider conformal structures invariant under a volumepreserving Anosov system. We show that if such a structure is in L for suffiently large p, then it is continuous.

The unit ball B is shown to be Gromov hyperbolic with respect to the Ferrand metric λBn and the modulus metric μBn , and dimension dependent upper bounds for the Gromov delta are obtained. In the two-dimensional case Gromov hyperbolicity is proved for all simply connected domains G. For λG also the case G = R n \ {0} is studied.

Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized N = 4 SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton–type representations of the 4d conformal algebra su(2, 2) is formulated in terms of a Bogolyubov ...