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Concept# Brane

Summary

In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge.
Mathematically, branes can be represented within , and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry.
p-branes
A point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one.
In addition to point particles and strings, it is possible to consider higher-dimensional branes. A p-dimensional brane is generally called "p-brane".
The term "p-brane" was coined by M. J. Duff et al. in 1988; "brane" comes from the word "membrane" which refers to a two-dimensional brane.
A p-brane sweeps out a (p+1)-dimensional volume in spacetime ca

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In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these s

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D-brane

In string theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named.

D-branes ar

D-branes ar

Related courses (1)

This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.

Recent proposals of large and infinite extra dimensions triggered a strong research activity in theories in which our universe is considered as a sub-manifold of some higher-dimensional space-time, a so-called 3-brane. In this context, it is generally assumed that some mechanism is at work which binds Standard Model particles to the 3-brane, an effect often referred to as the localization of matter on the brane. Gravity, however, is allowed to propagate in general also in the extra dimensions. As demonstrated by Randall and Sundrum in 1999, it is also possible to localize gravity itself on a 3-brane. In the setup they proposed. the 3-brane is realized as a singular domain wall separating two patches of 3-dimensional anti-de-Sitter (AdS5) space-time. The potential between two test masses on the brane at distances larger than the AdS5-radius was shown to be the usual 4-dimensional Newtonian 1/r potential with strongly suppressed corrections. The model of Randall and Sundrum, usually referred to as the Randall-Sundrum II setup, constitutes the center of interest for this thesis. The main goal of this work is to find possible generalizations to higher dimensions of the simple setup considered by Randall and Sundrum. One of the motivations for such a generalization is that a realistic theory should possibly be able to explain the chiral nature of 4-dimensional fermions on the brane. One way to explain chiral fermions from higher dimensions is to consider 3-braves identified with the cores of topological defects located in a higher-dimensional transverse space. Naturally a richer topological structure of the field configuration in transverse space provides the possibility of a more realistic spectrum of chiral fermions localized on the 3-brane. After two introductory chapters on extra dimensions and non-factorizable geometries which are relevant for the Randall-Sundrum II model, we briefly discuss basics of topological defects in the following third chapter. In the rest of the third chapter we consider various solutions to higher-dimensional Einstein equations coupled to a series of physically different sources and discuss their properties of localization of gravity. Due to their asymptotic nature, these solutions are only valid far from the cores of the defects in transverse space. Therefore, it seems reasonable to complement the consideration by presenting a particular numerical example of a solution to the Einstein equations coupled to a set of scalar and gauge fields: this solution describes a 3-brave realized as a 't Hooft-Polyakov monopole residing in the 3-dimensional transverse space of a 7-dimensional space-time. The last chapter of this work is dedicated to the study of a modification of the original Randall-Sundrum II model of another kind. The motivation is given by the geodesic incompleteness of the latter scenario with respect to time-like and light-like geodesics. We will describe a model which resembles the Randall-Sundrurn II model with respect to its properties of gravity localization but with the advantage that the underlying space-time manifold is geodesically complete. Parts of the calculations related to the properties of gravity at low energies in this model are rather technical in nature and we therefore preferred to assemble them in several appendices. We finally add some concluding remarks and discuss possible further developments.

We present a generalization of the Dvali-Gabadadze-Porrati scenario to higher codimensions which, unlike previous attempts, is free of ghost instabilities. The 4D propagator is made regular by embedding our visible 3-brane within a 4-brane, each with their own induced gravity terms, in a flat 6D bulk. The model is ghost-free if the tension on the 3-brane is larger than a certain critical value, while the induced metric remains flat. The gravitational force law "cascades" from a 6D behavior at the largest distances followed by a 5D and finally a 4D regime at the shortest scales.

2008Related lectures (2)

This thesis is devoted to studying field-theoretical branes in warped geometries, with emphasis on brane excitations and properties of background solutions. Firstly, we examine the features of a model in which our universe is represented by a local string-like defect embedded in a six-dimensional space-time with warped geometry. We demonstrate that in order to satisfy the dominant energy condition, the metric exterior to the defect's core must depend on its thickness. As a result of this dependence, in the limit of the string's thickness going to zero, either the solution no longer localizes the gravity on the defect, or the ratio of the six-dimensional Planck mass to the four-dimensional one diverges. Next, we propose and study a toy model allowing to investigate the phenomenon of quasilocalization. When applied to gravity, our setup can be seen as a (toy) model of a warped geometry in which the graviton is not fully localized on the brane. Studying the tensor sector of metric perturbations around this background, we find that its contribution to the effective gravitational potential is of four-dimensional type 1/r at intermediate scales and that at large scales it becomes 1/rα, 1