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Topological superconductors on superstring worldsheets
by Justin Kaidi, Julio Parra-Martinez, Yuji Tachikawa
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Submission summary
| Authors (as registered SciPost users): | Julio Parra-Martinez |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202002_00003v1 (pdf) |
| Date submitted: | 2020-02-18 01:00 |
| Submitted by: | Parra-Martinez, Julio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 $\rm 0$ string theory with $\Omega^2=(-1)^{\sf f}$ admits different GSO projections parameterized by $n$ mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of $n$ boundary Majorana fermions then leads to the classification of D-branes by $KO^n(X)\oplus KO^{-n}(X)$ 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 $\rm I$ worldsheet theory by studying the relevant bordism group, which classifies corresponding invertible phases. This paper provides the details for the results announced in the letter \cite{Kaidi:2019pzj}.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-6-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202002_00003v1, delivered 2020-06-07, doi: 10.21468/SciPost.Report.1743
Report
This paper has been a joy to read.
It offers a new approach to the systematic classification of closed string theories with N=(1,1) worldsheet supersymmetry, by relating them to topological fermion phases in two dimensions.
I highly recommend publication.
Report #1 by Anonymous (Referee 1) on 2020-4-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202002_00003v1, delivered 2020-04-24, doi: 10.21468/SciPost.Report.1640
Report
In this paper the authors provide a systematic understanding of GSO projection in
superstring theory by relating it to symmetry protected topological phases. Besides
providing us with a systematic classification of known string theories, this procedure
also gives new type 0 string theories. The authors' analysis also gives a systematic
way to classify the D-branes in these theories and derive their various
properties. They also give a natural description of the boundary degrees of freedom
of open strings on non-BPS branes, whose origin was somewhat obscure in the earlier
description of such D-branes. They also confirm their results using boundary state
construction of D-branes. This paper should definitely be published in SciPost.
I have one minor comment that the authors may want to take into account. For type I
string theory, the classification of stable D-branes using K-theory seems somewhat formal,
since it does not take into account possible tachyonic modes of the
open strings stretched between the D-brane under study and the
space-filling D9-branes that
must be present
for tadpole cancellation. For example type I D0-brane is stable but type I D8-brane
is expected to be unstable since the open strings connecting the D8-brane to the
D9-brane has $<4$ world-sheet fields satisfying ND boundary condition and we expect
their spectrum to contain a tachyon.
This issue will arise also in many of the unoriented type 0 theories, for
which the authors' analysis in appendix C shows that we need to add D9-branes to
cancel tadpoles.
This of course does not contradict any mathematical result since K-theory
gives classification
of stable D-branes in the presence of the orientifold plane but not in the presence of
D9-branes. As far as I can see, in the authors' analysis also the classification of stable
branes is done in absence of D9-branes. For example table 5 does not have a list of tachyons from the Dp-D9 strings. It will be better to state this explicitly to avoid confusion.
I also found one minor typo: the last term in the numerator of eq.(2.4) should be $-iE+m$.