A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A#H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A...

We prove that the open topological string partition function on aD-brane configuration in a Calabi-Yau manifoldX takes the form of a closed topological string partition function on a different Calabi-Yau manifold Xb. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by clo...

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. W...

In philology, both ‘sincerity’ and ‘cheng’ primarily mean, ‘to be true to oneself’. As a philosophical term, ‘sincerity’ roots in Aristotle’s ‘aletheutikos’. In medieval Europe, it is regarded as a neutral value that may either serve or disserve for ‘truth.’ As for Romantics, it is a positive value, and an individualistic concept whose two elements ‘true’ and ‘self’ refer to a person’s ‘true fe...

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. It turned out to be an adequate tool for the realization of the program of the study of Lie (super)algebras and associative algebras (and their representations), satisfying the sole locality property [K3]. The first basic definitions and...

We use data from Public Opinion Surveys on Household Financial Assets and Li-abilities from 1991 to 2002 to investigate the issues of unobserved heterogeneity amongcross-sectional units and stability of Japanese aggregate money demand function. Condi-tions that permit individual data and aggregate data to be modeled under one consistentformat are given. Alternative definitions o...

It is called shrinking, steady, or expanding soliton if a > 0, a = 0 or a < 0 respectively. More generally (M, g, f) is called a Bakry-Emery manifold if the so-called Bakry-Emery Ricci tensor Rcij + fij ≥ agij for some a ∈ R. In this paper we apply the modulus of continuity estimates developed in [AC,AC2,AC3] to give a different proof of an eigenvalue comparison estimate on Bakry-Emery manifold...

We construct new topological theories related to sigma models whose target space is a seven-dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six-dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. W...

We quantize the generators of the little subgroup of the asymptotic Poincaré group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy operator is densely defined on an appropriate Hilbert space, symmetric and essentially self-adjoint. Moreover, we prove a quantum analogue of the classical positivity of energy theorem due to Schoen ...