arXiv subjects

Brian Greene

Publications and source records attributed to Brian Greene.

23 records · Page 2Linked to original sources

arXiv2007

Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries

At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally tractable means of finding the Picard-Fuchs equations satisfied by the periods of all 3-forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self-contained.

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arXiv2006

Universal Correction to the Inflationary Vacuum

The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor $\exp(-βω_k)$ replaced by $\exp(ΔS)$, where $S$ is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine.

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arXiv2001

Split attractor flows and the spectrum of BPS D-branes on the Quintic

We investigate the spectrum of type IIA BPS D-branes on the quintic from a four dimensional supergravity perspective and the associated split attractor flow picture. We obtain some very concrete properties of the (quantum corrected) spectrum, mainly based on an extensive numerical analysis, and to a lesser extent on exact results in the large radius approximation. We predict the presence and absence of some charges in the BPS spectrum in various regions of moduli space, including the precise location of the lines of marginal stability and the corresponding decay products. We explain how the generic appearance of multiple basins of attraction is due to the presence of conifold singularities and give some specific examples of this phenomenon. Some interesting space-time features of these states are also uncovered, such as a nontrivial, moduli independent lower bound on the area of the core of arbitrary BPS solutions, whether they are black holes, empty holes, or more complicated composites.

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arXiv1997

String Theory on Calabi-Yau Manifolds

These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory which occur even at the classical level as well as those which require non-perturbative effects. These lecture notes are based on an evolving set of lectures presented at a number of schools but most closely follow a series of seven lectures given at the TASI-96 summer school on Strings, Fields and Duality.

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arXiv1994

On the Geometric Interpretation of N = 2 Superconformal Theories

We clarify certain important issues relevant for the geometric interpretation of a large class of N = 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.

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