Superstrings and Related Matters : Proceedings of the ICTP Spring Workshop, Trieste, Italy 27 March - 4 April 2000

214 Pages·2001·2.79 MB·English

by  Spring Workshop on Superstrings and Related Matters

abdus salam
international centre for theoretical physics
united nations educational, scientific international atomic
and cultural organization energy agency
Proceedings of the Trieste 2000 Spring Workshop on
UPERSTRINGS AND
RELATED MATTERS
Editors
C. Bachas
J. Maldacena
K. S. Narain
S. Randjbar-Daemi
World Scientific
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UPERSTRINGS AND
RELATED MATTERS

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international centre for theoretical physics
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Proceedings of the Trieste 2000 Spring Workshop on
UPERSTRINGS AND
RELATED MATTERS
ICTP, Trieste, Italy
27 March - 4 April 2000
Editors
C. Bachas
Ecole Normale Superieure, France
J. Maldacena
Harvard University, USA
K. S. Narain and S. Randjbar-Daemi
W Italy
V fe World Scientific
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Published by
World Scientific Publishing Co. Pte. Ltd.
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
SUPERSTR1NGS AND RELATED MATTERS
Proceedings of the ICTP Spring Workshop
Copyright © 2001 by The Abdus Salam International Centre for Theoretical Physics
ISBN 981-02-4525-4
Printed in Singapore by World Scientific Printers
V
PREFACE
The Abdus Salam ICTP's Spring Workshop, saw a variety of currently
interesting topics in string theory. These proceedings contain four sets of
lectures presented at this workshop.
GaberdiePs lectures contain a comprehensive introduction to the boundary
state approach to the D-branes and, in particular, non-BPS D-branes. Exam
ples are given that arise in the context of dualities between string theories.
Kachru's lectures deal with warped compactification in 5d theories and
the brane world scenarios that emerge. Gauge heirarchy and cosmological con
stant problems in this context are discussed in detail. Finally these lectures also
include string theory constructions that involve D-branes wrapped on various
cycles of Calabi-Yau spaces and the corresponding superpotential computa
tions in the world volume gauge theory are described. This is important for
both understanding supersymmetry breaking phenomenon as well as under
standing the quantum geometry of the Calabi-Yau spaces when the branes are
considered as probes.
Maldacena's lectures include a description of the holographic correspon
dence between field theories and string M theory. In particular, the correspon
dence between string/M theory compactification on AdS spaces and conformal
field theories living in the boundary, is discussed in detail. The evidences for
this correspondence are described in the context of maximally supersymmetric
gauge theories in 4d.
It is known that the effective world volume theory on D-branes in the pre
sence of NS-NS antisymmetric tensor field is a non-commutative gauge theory.
Nekrasov's lectures give a pedagogical introduction to this subject and, in
particular, focus on the non-perturbative solutions such as monopoles and
instantons in the non-commutative gauge theories.

vii
CONTENTS
Preface v
Lectures on Non-BPS Dirichlet Branes 1
M. R. Gaberdiel
Lectures on Warped Compactifications and Stringy Brane Constructions 43
S. Kachru
Large N Field Theories, String Theory and Gravity 74
J. Maldacena
Trieste Lectures on Solitons in Noncommutative Gauge Theories 141
N. A. Nekrasov
1
LECTURES ON NON-BPS DIRICHLET BRANES
MR. GABERDIEL
Department of Mathematics
King's College London
Strand, London WC2R 2LS, U. K.
A comprehensive introduction to the boundary state approach to Dirichlet branes
is given. Various examples of BPS and non-BPS Dirichlet branes are discussed. In
particular, the non-BPS states in the duality of Type IIA on K3 and the heterotic
string on T4 are analysed in detail.
1 Introduction
The past few years have seen a tremendous increase in our understanding of
the dynamics of superstring theory. In particular it has become apparent that
the five ten-dimensional theories, together with an eleven-dimensional theory
(M-theory), are different limits in moduli space of some unifying description.
A crucial ingredient in understanding the relation between the different per-
turbative descriptions has been the realisation that the solitonic objects that
define the relevant degrees of freedom at strong coupling are Dirichlet-branes
that have an alternative description in terms of open string theory.x'2'3
The D-branes that were first analysed were BPS states that break half the
(spacetime) supersymmetry. It has now been realised, however, that because
of their description in terms of open strings, D-branes can be constructed and
analysed in much more general situations. In fact, D-branes are essentially
described by a boundary conformal field theory4'5'6'7,8'9'10'11 (see also Refs. 12-
17 for earlier work in this direction), the consistency conditions of which are not
related to spacetime supersymmetry18'19'20 (for an earlier non-supersymmetric
orientifold construction see also Ref. 16). In an independent development, D-
branes that break supersymmetry have been constructed in terms of bound
states of branes and anti-branes by Sen21'22'23'24'25'26 (see also Ref. 27 for a
good review). This beautiful construction has been interpreted in terms of
K-theory by Witten,28 and this has opened the way for a more mathematical
treatment of D-branes. 29'30'31 It has also led the way to new insights into the
nature of the instability that is described by the open string tachyon.32
The motivation for studying D-branes that do not preserve spacetime su
persymmetry (and that are therefore sometimes called non-BPS D-branes) is
at least four-fold. First, in order to understand the strong/weak coupling
dualities of supersymmetric string theories in more detail, it is important to
2
analyse how these dualities act on states that are not BPS saturated. After
all, the behaviour of the BPS states at arbitrary coupling is essentially deter
mined by spacetime supersymmetry (provided that it remains unbroken for
all values of the coupling constant), and thus one is not really probing the
underlying string theory unless one also understands how non-BPS states be
have at strong coupling. The dualities typically map perturbative states to
non-perturbative (D-brane type) states, and thus one will naturally encounter
non-BPS D-branes in these considerations.
The second motivation is related to the question of whether string duality
should intrinsically only apply to supersymmetric string theories, or whether
also non-supersymmetric theories should be related by duality. This is cer
tainly, a priori, an open question" it is conceivable that spacetime super-
symmetry is a crucial ingredient without which there is no reason to believe
that these dualities should exist, but it is also conceivable that spacetime su
persymmetry is just a convenient tool that allows one to use sophisticated
arguments and techniques to verify conjectures that are otherwise difficult to
check. Dirichlet branes play a central role in the understanding of string du
alities, and if one wants to make progress on this question, it is important to
develop techniques to analyse and describe Dirichlet branes without reference
to spacetime supersymmetry.
Thirdly, one of the interesting implications of the Maldacena conjecture39
is that one can obtain non-trivial predictions about field theory from string
theory. In the original formulation this was applied to supersymmetric string
and field theories, but it is very tempting to believe that similar insights may
be gained for non-supersymmetric theories. This line of thought has been
developed recently, starting with a series of papers by Klebanov & Tseytlin.20
Finally, non-BPS D-branes offer the intriguing possibility of string com-
pactifications in which supersymmetry is preserved in the bulk but broken on
the brane. Various orientifold models involving branes and anti-branes have
been constructed recently,40,41'42,43 but it is presumably also possible to con
struct interesting models involving non-BPS D-branes. (Non-BPS -branes in
Type II theories have recently been considered in Refs. 44 and 45.) The fact
that at specific points in the moduli space their spectrum is Bose-Fermi de
generate may be of significance in this context.46
The main aim of these lectures is to explain the boundary state approach to
D-branes, and to give some applications of it, in particular to the construction
of non-BPS D-branes. The structure of the lectures is as follows. In section 2
we explain carefully the underpinnings of the boundary state approach and
"Recently, some suggestive proposals have however been made.18''