Report for the Academic Year 1992-1993 - The Institute Libraries ...

THE SCHOOL OF NATURAL SCIENCES
invariance for the classical equations of motion, as expected. Professor Witten
showed that an antibracket (in the sense of Batalin and Vilkovisky) on the space
of two dimensional field theories is the main structure needed to carry this out.
Professor Witten has pursued this matter in two subsequent papers. In "Some
Computations In Background Independent Off-Shell String Theory," he made
the definition of the string field action concrete in some cases in which ultraviolet
divergences are not a problem. In a forthcoming paper, five-year Member Keke
Li and Professor Witten investigate the role of the ultraviolet divergences (and
thus the crucial, unsolved problem (a) mentioned above) in a special situation.
(2) Professor Witten once again has been working on properties of the N=2
superconformal models that are used in making models of particle physics from
string theory. He made several contributions.
(a) In "Phases Of N=2 Theories In Two Dimensions," he gave a much better
explanation of the relation of Calabi-Yau and Landau-Ginzburg models than had
existed previously. It turned out, unexpectedly, that this gave rise to insights
about some apparently different questions, such as the occurrence of topology-
changing processes in physics, that is processes in which the topology of space-
time changes. (Along with parallel work by Paul Aspinwall, Brian Green, and
David Morrison here at the Institute, which will be mentioned shortly, this
development was featured in the February 27 issue of Science News magazine.)
Professor Witten thinks this work makes the whole theory of string theory on
Calabi-Yau manifolds much more beautiful. Some aspects of this work may also
prove to have applications relatively close to phenomenology.
(b) In "Landau-Ginzburg Models and N=2 Minimal Models," Professor Witten
has obtained a much better understanding of the Landau-Ginzburg description
of A/=2 minimal models in two dimensions than had existed previously.
(c) In a forthcoming paper, "On Quantum Background Independence In String
Theory," he analyzes the "holomorphic anomaly" recently found by Bershadsky,
Cecotti, Ooguri, and Vafa as an obstruction to ordinary background indepen-
dence in certain topological field theories. He also proposes a more exotic sense
in which background independence does hold in this situation. Professor Witten
hopes that this phenomenon may be relevant to ordinary background indepen-
dence in string theory, the question addressed in (1) above.
Professor Witten notes that we have had a mini-workshop on mirror symmetry
(a remarkable non-classical relation between different space-times that is possible
in string theory) here at the Institute this year, with the participation of Aspin-
wall, Morrison, and Greene. They made a fundamental discovery using mirror
symmetry to predict the possibihty of change in the topology of space-time; this
43