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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-10-20 19:29:13 +02:00
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sec/part2/introduction.tex
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@@ -56,7 +56,7 @@ The $n$-dimensional \emph{orbifold} $\ccO$ is finally defined as a paracompact H
In string theory the notion of orbifold has a more stringent characterisation with respect to pure mathematics.
Differently from the general definition, orbifolds in physics usually appear as a global orbit space $M / G$ where $M$ is a manifold and $G$ the group of its isometries, often leading to the presence of \emph{fixed points} (i.e.\ points in the manifold which are left invariant by the action of $G$) where singularities emerge due to the presence of additional degrees of freedom given by \emph{twisted states} of the string~\cite{Dixon:1985:StringsOrbifolds,Dixon:1986:StringsOrbifoldsII}.
They are commonly introduced as singular limits of \cy manifolds~\cite{Candelas:1985:VacuumConfigurationsSuperstrings}, which in turn can be recovered using algebraic geometry to smoothen the singular points.
However they can also be used to model peculiar time-dependent backgrounds~\cite{Horowitz:1991:SingularStringSolutions,Khoury:2002:BigCrunchBig,Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,Cornalba:2002:NewCosmologicalScenario,Cornalba:2004:TimedependentOrbifoldsString,Craps:2006:BigBangModels,Bachas:2002:NullBraneIntersections,Bachas:2003:RelativisticStringPulse}.
However they can also be used to model peculiar time-dependent backgrounds~\cite{Horowitz:1991:SingularStringSolutions,Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,Cornalba:2002:NewCosmologicalScenario,Cornalba:2004:TimedependentOrbifoldsString,Craps:2006:BigBangModels,Bachas:2002:NullBraneIntersections,Bachas:2003:RelativisticStringPulse}.
They are in fact good toy models to study Big Bang scenarios in string theory.
We focus specifically on the study of such cosmological singularities in the framework of string theory defined on time-dependent orbifolds.