The Phase Transitions and the Moduli Space of Particles from D- Brane (original) (raw)

MATHEMATICAL ASPECTS OF D-BRANES ∗ hep-th/0402023

2004

In this lecture we review recent work on describing D-branes with nonzero Higgs vevs in terms of sheaves, which gives a physical on-shell D-brane interpretation to more sheaves than previously understood as describing D-branes. The mathematical ansatz for this encoding is checked by comparing open string spectra between D-branes with nonzero Higgs vevs to Ext groups between the corresponding sheaves. We illustrate the general methods with a few examples. 1.

Spectra of D-branes with Higgs vevs

Advances in Theoretical and Mathematical Physics, 2004

In this paper we continue previous work on counting open string states between D-branes by considering open strings between D-branes with nonzero Higgs vevs, and in particular, nilpotent Higgs vevs, as arise, for example, when studying D-branes in orbifolds. Ordinarily Higgs vevs can be interpreted as moving the D-brane, but nilpotent Higgs vevs have zero eigenvalues, and so their interpretation is more interesting -for example, they often correspond to nonreduced schemes, which furnishes an important link in understanding old results relating classical D-brane moduli spaces in orbifolds to Hilbert schemes, resolutions of quotient spaces, and the McKay correspondence. We give a sheaf-theoretic description of D-branes with Higgs vevs, including nilpotent Higgs vevs, and check that description by noting that Ext groups between the sheaves modelling the D-branes, do in fact correctly count open string states. In particular, our analysis expands the types of sheaves which admit on-shell physical interpretations,

Superconformal D-branes and moduli spaces

2003

The on-going quest for a single theory that describes all the forces of nature has led to the discovery of string theory. This is the only known theory that successfully unifies gravity with the electroweak and strong forces. It postulates that the fundamental building blocks of nature are strings, and that all particles arise as different excitations of strings. This theory is still poorly understood, especially at strong coupling, but progress is being made all the time. One breakthrough came with the discovery of extended objects called D-branes, which have proved crucial in probing the strong-coupling regime. They are instrumental in realising dualities (equivalences) between different limits of string theory.

Novel Perspectives in String Phenomenology

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019), 2020

String theory is the leading contemporary framework to explore the synthesis of quantum mechanics with gravity. String phenomenology aims to study string theory while maintaining contact with observational data. The fermionic Z 2 × Z 2 orbifold provides a case study that yielded a rich space of phenomenological models. String theory in ten dimensions gives rise to non-supersymmetric tachyonic vacua that may serve as good starting points for the construction of phenomenologically viable models. I discuss an example of such a three generation standard-like model in which all the moduli, aside from the dilaton, are frozen. The Möbius symmetry may turn out to play a central role in the synthesis of quantum mechanics and gravity. In a local version it plays a central role in string theory. In a global version it underlies the Equivalence Postulate of Quantum Mechanics (EPOQM) formalism, which implies that spatial space is compact. It was recently proposed that evidence that the universe is closed exists in the Cosmic Microwave Background Radiation [1, 2].

D-branes, orbifolds, and Ext groups

Nuclear Physics B, 2003

In this note we extend previous work on massless Ramond spectra of open strings connecting D-branes wrapped on complex manifolds, to consider D-branes wrapped on smooth complex orbifolds. Using standard methods, we calculate the massless boundary Ramond sector spectra directly in BCFT, and find that the states in the spectrum are counted by Ext groups on quotient stacks (which provide a notion of homological algebra relevant for orbifolds). Subtleties that cropped up in our previous work also appear here. We also use the McKay correspondence to relate Ext groups on quotient stacks to Ext groups on (large radius) resolutions of the quotients. As stacks are not commonly used in the physics community, we include pedagogical discussions of some basic relevant properties of stacks.

Lectures on D-branes and Sheaves

arXiv: High Energy Physics - Theory, 2003

These notes are a writeup of lectures given at the twelfth Oporto meeting on “Geometry, Topology, and Physics,” and at the Adelaide workshop “Strings and Mathematics 2003,” primarily geared towards a physics audience. We review current work relating boundary states in the open string B model on Calabi-Yau manifolds to sheaves. Such relationships provide us with a mechanism for counting open string states in situations where the physical spectrum calculation is essentially intractable – after translating to mathematics, such calculations become easy. We describe several different approaches to these models, and also describe how these models are changed by varying physical circumstances – flat B field backgrounds, orbifolds, and nonzero Higgs vevs. We also discuss mathematical interpretations of operator products, and how such mathematical interpretations can be checked physically. One of the motivations for this work is to understand the precise physical relationship between boundar...

Mathematical Aspects of D-Branes

Quantum Theory and Symmetries, 2004

Introductory Lectures on D-Branes

2002

This is a pedagogical introduction to D-branes, addressed to graduate students in field theory and particle physics and to other beginners in string theory. I am not going to review the most recent results since there are already many good papers on web devoted to that. Instead, I will present some old techniques in some detail in order to show how some basic properties of strings and branes as the massless spectrum of string, the effective action of D-branes and their tension can be computed using QFT techniques. Also, I will present shortly the boundary state description of D-branes. The details are exposed for bosonic branes since I do not assume any previous knowledge of supersymmetry which is not a requirement for this school. However, for completeness and to provide basic notions for other lectures, I will discuss the some properties of supersymmetric branes. The present lectures were delivered at Jorge André Swieca School on Particle and Fields, 2001, Campos do Jordão, Brazil.

Introductory Lectures to D-branes

2001

On D-brane dynamics and moduli stabilization

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of T6/Z3 orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in T6/Z3 orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of "brane supersymmetry breaking", and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kahler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kahler moduli stabilization, this is not always the case.

The Phase Transitions and the Moduli Space of Particles from D- Brane (original) (raw)

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