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Spin structures and baby universes

Balasubramanian, Vijay; Kar, Arjun; Ross, Simon F.; Ugajin, Tomonori

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Vijay Balasubramanian

Arjun Kar

Tomonori Ugajin


We extend a 2d topological model of the gravitational path integral to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space, and vanishes when the number of R boundaries is odd. This vanishing implies a non-factorization of the correlator, which necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes, for which the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving “spacetime D-branes”. We extend our ideas to Jackiw-Teitelboim gravity, and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.


Balasubramanian, V., Kar, A., Ross, S. F., & Ugajin, T. (2020). Spin structures and baby universes. Journal of High Energy Physics, 2020(9), Article 192.

Journal Article Type Article
Acceptance Date Sep 2, 2020
Online Publication Date Sep 30, 2020
Publication Date 2020-09
Deposit Date Oct 7, 2020
Publicly Available Date Oct 7, 2020
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 9
Article Number 192
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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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