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Spin structures and baby universes

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

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Authors

Vijay Balasubramanian

Arjun Kar

Tomonori Ugajin



Abstract

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.

Citation

Balasubramanian, V., Kar, A., Ross, S. F., & Ugajin, T. (2020). Spin structures and baby universes. Journal of High Energy Physics, 2020(9), Article 192. https://doi.org/10.1007/jhep09%282020%29192

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
DOI https://doi.org/10.1007/jhep09%282020%29192
Related Public URLs https://arxiv.org/abs/2007.04333

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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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