33 research outputs found
Homotopy algebra of open-closed strings
This paper is a survey of our previous works on open-closed homotopy
algebras, together with geometrical background, especially in terms of
compactifications of configuration spaces (one of Fred's specialities) of
Riemann surfaces, structures on loop spaces, etc. We newly present Merkulov's
geometric A_infty-structure [Internat. Math. Res. Notices (1999) 153--164,
arxiv:math/0001007] as a special example of an OCHA. We also recall the
relation of open-closed homotopy algebras to various aspects of deformation
theory.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Homotopy algebras inspired by classical open-closed string field theory
We define a homotopy algebra associated to classical open-closed strings. We
call it an open-closed homotopy algebra (OCHA). It is inspired by Zwiebach's
open-closed string field theory and also is related to the situation of
Kontsevich's deformation quantization. We show that it is actually a homotopy
invariant notion; for instance, the minimal model theorem holds. Also, we show
that our open-closed homotopy algebra gives us a general scheme for deformation
of open string structures (A(infinity)-algebras) by closed strings
(L(infinity)-algebras).Comment: 30 pages, 14 figures; v2: added an appendix by M.Markl, ambiguous
terminology fixed, minor corrections; v3: published versio
Matrix Factorizations and Representations of Quivers II: type ADE case
We study a triangulated category of graded matrix factorizations for a
polynomial of type ADE. We show that it is equivalent to the derived category
of finitely generated modules over the path algebra of the corresponding Dynkin
quiver. Also, we discuss a special stability condition for the triangulated
category in the sense of T. Bridgeland, which is naturally defined by the
grading.Comment: v2: typos corrected, added an appendix by K.Ued
Exact Tachyon Condensation on Noncommutative Torus
We construct the exact noncommutative solutions on tori. This gives an exact
description of tachyon condensation on bosonic D-branes, non-BPS D-branes and
brane-antibrane systems. We obtain various bound states of D-branes after the
tachyon condensation. Our results show that these solutions can be generated by
applying the gauge Morita equivalence between the constant curvature projective
modules. We argue that there is a general framework of the noncommutative
geometry based on the notion of Morita equivalence which underlies this
specific example.Comment: Latex 31 pages, v2: presentation much improved, various points
clarifie
Comments on Large N Matrix Model
The large N Matrix model is studied with attention to the quantum
fluctuations around a given diagonal background. Feynman rules are explicitly
derived and their relation to those in usual Yang-Mills theory is discussed.
Background D-instanton configuration is naturally identified as a
discretization of momentum space of a corresponding QFT. The structure of large
N divergence is also studied on the analogy of UV divergences in QFT.Comment: 32 pages, 9 figure