geometry and physics of branes

[...]... in Trieste, the University of Insubria (Como-Varese), the Department of Chemistry, Physics and Mathematics of the same University and the Physics Departments of the Universities of Milan, Pavia and Turin We are grateful to the other members of the scientific organizing committee Mauro Carfora, Pietro Fre’, Alberto Lerda and Augusto Sagnotti and to the scientific coordinator of the Centro Volta, Giulio... emphasize that the twofold interpretation of the D -branes, as classical supergravity solutions and as spacetime defects where open strings can terminate, is a direct consequence of a duality between open and closed strings which allows a double interpretation of the annulus/cylinder diagram This twofold nature of the D -branes is their most important and intriguing feature; indeed because of this they play... supergravity field equations of type IIA or IIB that are charged under one of the antisymmetric potentials of the R–R sector It has been well known for a long time that no perturbative configuration of string theory can carry charge under the R–R potentials and thus the discovery of D -branes has represented a remarkable breakthrough in our understanding of string theory and, in particular, of its nonperturbative... has to expand the exponential and then ˜ antisymmetrize the indices of the -matrices Finally, |A | B stands for the spinor 1 We would like to remark that the overlap equations vacuum of the R–R sector (3.9) and (3.10) do not allow us to determine the overall normalization of the boundary state, and not even to get the Born–Infeld prefactor of equation (3.12) The latter can be introduced by hand as in... from a gravitational point of view (i.e in a theory of closed strings) and from a gauge field theory point of view (i.e in a theory of open strings) This open/closed string duality is at the heart of the gauge/gravity correspondence which has recently been uncovered since Maldacena’s well-known conjecture [14–16] and which is perhaps one of the most exciting developments of string theory In this contribution... properties and interactions of the Dbranes, both in flat and in curved backgrounds (see, for example, [10–12] or the reviews in [13] and the references therein) In particular, in [10, 12] it has been shown that the boundary state encodes all relevant properties of the classical Dbranes since it correctly reproduces the couplings of the Dirac–Born–Infeld action as well as the large-distance behaviour of the... generalization of Dirac’s quantization condition of the electric charge (suitably written for the type II string effective actions with coupling constant 2 2κ10 ), from which we can deduce that a D p-brane and a D(6 − p)-brane are electromagnetically dual to each other 2.3.4 The geometry of the D3-brane of type IIB In this section we recall some peculiar features of the spacetime geometry produced by the D3 -branes. .. define z = L 2 /r , the part of the previous metric in square brackets can be rewritten as L2 z2 (dx a dx b ηab + dz 2 ) (2.72) 20 Branes in string theory This is one of the standard forms in which the metric of a five-dimensional anti-de Sitter spacetime of radius L is usually written Therefore, at distances r L the geometry produced by N D3 -branes appears as the product of a fivedimensional anti-de... I-15100 Alessandria (Italy) In recent years there has been a remarkable improvement in our understanding of string theory One of the key ingredients of this progress has been the concept of duality [1], originally formulated for the supersymmetric gauge field theories and later extended to string theory [2] Among other things, the idea of duality has led to the conclusion that the five consistent and perturbatively... definition of κ we implicitly declare 10 that the field φ that appears in the action (2.1) represents only the fluctuation of the dilaton around its vacuum expectation value Branes in string theory 8 In this frame the curvature term has the standard form of the Einstein–Hilbert action and the dilaton field also has a canonical normalization factor of − 1 The 2 price one has to pay for this is the appearance of . alt="" GEOMETRY AND PHYSICS OF BRANES Series in High Energy Physics, Cosmology and Gravitation Other books in the series Electron–Positron Physics at the Z M G Green, S L Lloyd, P N Ratoff and D. of Cosmic Strings Cosmic Strings in the Wire Approximation M R Anderson The Galactic Black Hole Lectures on General Relativity and Astrophysics H Falcke and F W Hehl GEOMETRY AND PHYSICS OF BRANES Edited. the University of Insubria (Como-Varese), the Department of Chemistry, Physics and Mathematics of the same University and the Physics Departments of the Universities of Milan, Pavia and Turin. We