Math @ Duke

Publications [#9794] of Eric Sharpe
Preprints
 Eric Sharpe, String Orbifolds and Quotient Stacks
, preprint 2001 [hepth/0102211]
(last updated on 2001/03/01)
Abstract: In this note we observe that, contrary to the usual lore,
string orbifolds do not describe strings on quotient spaces,
but rather seem to describe strings on objects called
quotient stacks, a result that follows simply from
unraveling definitions, and is further justified by a number
of results. Quotient stacks are very closely related to
quotient spaces; for example, when the orbifold group acts
freely, the quotient space and the quotient stack are
homeomorphic. We explain how sigma models on quotient
stacks naturally have twisted sectors, and why a sigma model
on a quotient stack would be a nonsingular CFT even when
the associated quotient space is singular. We also show how
to understand twist fields in this language, and outline the
derivation of the orbifold Euler characteristic purely in
terms of stacks. We also outline why there is a sense in
which one naturally finds B nonzero on exceptional divisors
of resolutions. These insights are not limited to merely
understanding existing string orbifolds: we also point out
how this technology enables us to understand orbfiolds in
Mtheory, as well as how this means that string orbifolds
provide the first example of an entirely new class of string
compactifications. As quotient stacks are not a staple of
the physics literature, we include a lengthy tutorial on
quotient stacks.


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