Annual Report 2005 - Fields Institute - University of Toronto

Dam Son (Washington)
QCD and a holographic model of hadrons
Tadashi Takayanagi (Harvard)
Arkady Tseytlin (Ohio State)
Semiclassical approach to AdS/CFT
Course on Mirror Symmetry
September–December 2004
Instructor: Kentaro Hori (Toronto)
The course gave an introduction to mirror symmetry in the
context of string theory. It was designed to start up activity
of the year-long Program on the Geometry of String
Theory and was followed by graduate students as well as
participants of the thematic program. Since the subject is
currently under active investigation in theoretical physics
and mathematics, one goal of the course was to point out
the connections between the two approaches and to stimulate
collaboration between researchers of both fields.
Beginning with an introduction to superconformal field
theories, for example on Calabi-Yau manifolds, and the
twisting to topological field theories, the course built up
the foundations in order to state the conjecture of Mirror
Symmetry as a duality between two superconformal field
theories. It gave a physical explanation of the conjecture in
terms of gauged linear sigma models and provided a number
of examples of mirror pairs. The course closed with
some aspects of mirror symmetry including non-perturbative
extended objects such as D-branes in this context.
Course on String Theory
September–December 2004
Instructor: Amanda Peet (Toronto)
String theory research began its life at the University of
Toronto in the year 2000, and has been revving up since
then. The international spotlight has shone particularly
brightly on UofT and the Fields Institute in the academic
year 2004-5, during the Theme Year on “The Geometry of
String Theory” and for the final event “Strings 2005” in
July. One of the primary groups of people benefiting from
all of this activity was local graduate students - in both
physics and mathematics. In order to ensure that junior
students could benefit maximally, an introductory course
on string theory was proposed, planned, and then taught in
the Fall semester by Prof. Amanda Peet.
T h e m a t i c P r o g r a m s
PHY2406F “Introduction to String Theory” was offered
as a semester-long Physics course in the Fall of 2004-5. To
enable students to commute to class from other Ontario
universities, lectures were held in a two-hour block on Fridays
with office hours later the same day. Six students took
the course for credit: four at the University of Toronto and
two at the University of Waterloo. There were a large number
of auditors: approximately 40 at the beginning of the
semester, later decreasing to a core about half a dozen who
came to every single class along with registered students.
Auditors included faculty, postdocs, graduate students,
and even one undergraduate. The course textbook was the
brand-new “A First Course in String Theory” by Barton
Zwiebach of MIT (Cambridge, 2004). All lecture notes were
offered in digital form on the course web hub.
Since PHY2406F was designed to serve junior graduate
students, no graduate-level prerequisites were assumed. In
particular, this course was taught alongside other standard
graduate courses in high-energy theoretical physics such as
quantum field theory and general relativity. Accordingly,
the course began with a lightning overview of classical
physics of non-relativistic and relativistic particles. This
segued into the classical physics of non-relativistic and
relativistic strings, with particular attention to gauge fixing
in light-front gauge. Next came quantization in light-front
gauge, starting with a discussion of free quantum fields of
spin zero, one and two. The final dress rehearsal was quantization
of the relativistic point particle.
Then came the part everyone was waiting for: quantization
of the relavistic string. Worldsheet symmetries were a concentration.
Closed strings and open strings were separately
discussed, before worldsheet fermions and the superstring
was introduced in the NSR formalism. The course then
shifted gears to study of the more recent topic of D-branes.
Gauge fields on many D-branes were a major focus, including
quantization of strings stretched between different
D-branes and hence possessing worldsheet different boundary
conditions at their endpoints. Next came T-duality,
circle compactification, and the Hagedorn phenomenon.
Supergravity as the low-energy limit of string theory and
black p-branes was introduced. This laid the groundwork
for an explanation of one of the most famous results from
string theory: computation from quantum statistical
mechanics of strings and D-branes of the thermodynamic
entropy of wide classes of black holes. Superstring duality,
compactifications, and the gravity/gauge correspondences
such as AdS/CFT rounded out the final section of the
course.
Fields Institute 2005 ANNUAL REPORT 16