IPMU Komaba Seminar

Speaker: Makoto Sakurai (The Univ. of Tokyo)
Title: Differential Graded Categories and heterotic string theory
Date (JST): Mon, Nov 09, 2009, 16:30 - 18:00
Place: Room 002, Mathematical Sciences Building, Komaba Campus
Abstract: The saying "category theory is an abstract nonsense" is even
physically not true. The schematic language of triangulated category
presents a new stage of string theory. To illuminate this idea, I will
draw your attention to the blow-up minimal model of complex algebraic
surfaces. This is done under the hypothetical assumptions of
"generalized complex structure" of cotangent bundle due to Hitchin
school. The coordinate transformation Jacobian matrices of the measure
of sigma model with spin structures cause one part of the
gravitational "anomaly cancellation" of smooth Kahler manifold $X$ and
Weyl anomaly of compact Riemann surface $\Sigma$. $Anom = c_1 (X) c_1
(\Sigma) \oplus ch_2 (X)$, in terms of 1st and 2nd Chern
characters. Note that when $\Sigma$ is a puctured disk with flat
metric, the chiral algebra is nothing but the ordinary vertex
algebra. Note that I do not explain the complex differential geometry,
but essentially more recent works with the category of DGA
(Diffenreial Graded Algebra), which is behind the super conformal
field theory of chiral algebras. My result of "vanishing tachyon"
(nil-radical part of vertex algebras) and "causality resortation" in
compactified non-critical heterotic sigma model is physically a
promising idea of new solution to unitary representation of operator
algebras. This idea is realized in the formalism of BRST cohomology
and its generalization in $\mathcal{N} = (0,2)$ supersymmetry, that
is, non-commutative geometry with non-linear constraint condition of
pure spinors for covariant quantization.