63 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
Noether's variational theorem II and the BV formalism
We review the basics of the Lagrangian approach to field theory and recast
Noether's Second Theorem formulated in her language of dependencies using a
slight modernization of terminology and notation. We then present the
Cattaneo-Felder sigma model and work out the Noether identities or dependencies
for this model. We review the description of the Batalin-Vilkovisky formalism
and show explicitly how the anti-ghosts encode the Noether identities in this
example.Comment: 15 pages, submitted to the Proceedings of the 2002 Winter School
``Geometry and Physics'', Srni, Czech Republi
Sh-Lie algebras Induced by Gauge Transformations
The physics of ``particles of spin '' leads to representations of a
Lie algebra of gauge parameters on a vector space of fields.
Attempts to develop an analogous theory for spin have failed; in fact,
there are claims that such a theory is impossible (though we have been unable
to determine the hypotheses for such a `no-go' theorem). This led BBvD
[burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent
parameters' in a setting where some analysis in terms of smooth functions is
possible. Having recognized the resulting structure as that of an sh-lie
algebra (-algebra), we have now reproduced their structure entirely
algebraically, hopefully shedding some light on what is going on.Comment: Now 24 pages, LaTeX, no figures Extensively revised in terms of the
applications and on shell aspects. In particular, a new section 8 analyzes
Ikeda's 2D example from our perspective. His bracket is revealed as a
generalized Kirillov-Kostant bracket. Additional reference
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