Spin structures and baby universes

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

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
• Electronic ISSN: 1029-8479
• 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
• Public URL: https://durham-repository.worktribe.com/output/1254810
• Related Public URLs: https://arxiv.org/abs/2007.04333