The simplest toroidally compactified string theories exhibit a duality between small and large radii: compactification on a circle, for example, is invariant under R → 1/(2R). Compactification on more general Lorentzian lattices (e.g. toroidal compactification in the presence of background metric, antisymmetric tensor, and gauge fields) yields theories for which a large-small equivalence is not...

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space R/Γ as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group Γ on Euclidean space Rd and a projective representation U of Γ. The choice of Hilbert space on ...

In this paper we construct the analogue of Dedekind η−function on the moduli space of polarized CY manifolds. We prove that the L norm of η(τ ) is the regularized determinants of the Laplacians of the CY metric on (0, 1) forms. We construct the analogue of the Baily-Borel Compactification of the moduli space of polarized CY and prove that it has the same properties as the Baily-Borel compactifi...

While primordial life is thought to have been RNA-based (Cech, Cold Spring Harbor Perspect. Biol. 4 (2012) a006742), all living organisms store genetic information in DNA, which is chemically more stable. Distinctions between the RNA and DNA worlds and our views of "DNA" synthesis continue to evolve as new details emerge on the incorporation, repair and biological effects of ribonucleotides in ...

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson found in [And03] and [And06]. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the com...