Quantisation of Super Teichmüller Theory

Aghaei, Nezhla; Pawelkiewicz, Michal; Teschner, J.

doi:10.1007/s00220-017-2883-0

Cited by 8 publications

(8 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unlike bosonic Teichmüller space, the superanalogue ST (Σ) is not connected, but has multiple connected components labeling spin structures on Σ. See, e.g.,[72,86] for recent work.…”

mentioning

confidence: 99%

Supergroup structure of Jackiw-Teitelboim supergravity

Fan

Mertens

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

We develop the gauge theory formulation of $$ \mathcal{N} $$ N = 1 Jackiw-Teitelboim supergravity in terms of the underlying OSp(1|2, ℝ) supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of OSp(1|2, ℝ) is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of OSp(1|2, ℝ) and show that whereas the corresponding Plancherel measure does not match the density of states of $$ \mathcal{N} $$ N = 1 JT supergravity, a restriction to the positive subsemigroup OSp+(1|2, ℝ) yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity.

show abstract

“…Unlike bosonic Teichmüller space, the superanalogue ST (Σ) is not connected, but has multiple connected components labeling spin structures on Σ. See, e.g.,[72,86] for recent work.…”

mentioning

confidence: 99%

Supergroup structure of Jackiw-Teitelboim supergravity

Fan

Mertens

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Unlike bosonic Teichmüller space, its super-analogue ST (Σ) is not connected, but has multiple connected components labeling spin structures on Σ. See, e.g.,[83,84] for recent work.…”

mentioning

confidence: 99%

Supergroup Structure of Jackiw-Teitelboim Supergravity

Fan,

Mertens

2021

Preprint

View full text Add to dashboard Cite

We develop the gauge theory formulation of N = 1 Jackiw-Teitelboim supergravity in terms of the underlying OSp(1|2, R) supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of OSp(1|2, R) is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of OSp(1|2, R) and show that whereas the corresponding Plancherel measure does not match the density of states of N = 1 JT supergravity, a restriction to the positive subsemigroup OSp + (1|2, R) yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity.

show abstract

“…In this section, we describe the quantization of the super Teichmüller theory (as discussed in [25]). We again discuss the case of the once-punctured torus.…”

Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " I O A P E V I G U ...mentioning

confidence: 99%

“…In physics language, this is to adopt the Hamiltonian formulation of the theory. Fortunately, the associated "Hilbert space" H(Σ) associated with a punctured spin 2-manifold Σ has already been constructed in the literature in the context of the quantum super Teichmüller theory [25] and we will use this as a starting point of our discussion.…”

Section: Outline Of Strategymentioning

confidence: 99%

“…One such generalization is to consider the super Teichmüller theory, which studies the moduli space of super Riemann surfaces. While the super Teichmüller space has long been playing fundamental roles in the perturbative superstring theory, the systematic analysis of explicit classical coordinate systems [23,24] and the quantization [25,26] are relatively new subjects. 2 The goal of the present paper, stimulated by recent developments, is to consider the super Teichmüller counterpart of the Teichmüller TQFT.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards Super Teichmüller Spin TQFT

Aghaei,

Pawelkiewicz,

Yamazaki

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin 3-manifold geometries, by taking advantage of the recent results on the quantization of the super Teichmüller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin 3-manifolds. We also comment on the relations of the super Teichmüller spin TQFT to 3dimensional Chern-Simons theories with complex gauge groups, and to a class of 3d N = 2 theories as arising from the compactifications of the M5-branes.

show abstract

Quantisation of Super Teichmüller Theory

Cited by 8 publications

References 35 publications

Supergroup structure of Jackiw-Teitelboim supergravity

Supergroup structure of Jackiw-Teitelboim supergravity

Supergroup Structure of Jackiw-Teitelboim Supergravity

Towards Super Teichmüller Spin TQFT

Contact Info

Product

Resources

About