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Topological superconductors on superstring worldsheets
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We point out that different choices of Gliozzi-Scherk-Olive (GSO)
projections in superstring theory can be conveniently understood by the
inclusion of fermionic invertible phases, or equivalently topological
superconductors, on the worldsheet. This allows us to find that the
unoriented Type
0
0
string theory with
\Omega^2=(-1)^{f}
Ω
2
=
(
−
1
)
f
admits different GSO projections parameterized by
n
n
mod 8, depending on the number of Kitaev chains on the worldsheet. The
presence of
n
n
boundary Majorana fermions then leads to the classification of D-branes
by
KO^n(X)\oplus KO^{-n}(X)
K
O
n
(
X
)
⊕
K
O
−
n
(
X
)
in these theories, which we also confirm by the study of the D-brane
boundary states. Finally, we show that there is no essentially new GSO
projection for the Type
I
I
worldsheet theory by studying the relevant bordism group, which
classifies corresponding invertible phases. In two appendixes the
relevant bordism group is computed in two ways.
Title: Topological superconductors on superstring worldsheets
Description:
We point out that different choices of Gliozzi-Scherk-Olive (GSO)
projections in superstring theory can be conveniently understood by the
inclusion of fermionic invertible phases, or equivalently topological
superconductors, on the worldsheet.
This allows us to find that the
unoriented Type
0
0
string theory with
\Omega^2=(-1)^{f}
Ω
2
=
(
−
1
)
f
admits different GSO projections parameterized by
n
n
mod 8, depending on the number of Kitaev chains on the worldsheet.
The
presence of
n
n
boundary Majorana fermions then leads to the classification of D-branes
by
KO^n(X)\oplus KO^{-n}(X)
K
O
n
(
X
)
⊕
K
O
−
n
(
X
)
in these theories, which we also confirm by the study of the D-brane
boundary states.
Finally, we show that there is no essentially new GSO
projection for the Type
I
I
worldsheet theory by studying the relevant bordism group, which
classifies corresponding invertible phases.
In two appendixes the
relevant bordism group is computed in two ways.
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