Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$

Abstract

We study Matrix Quantum Mechanics on the Euclidean time orbifold $S_1/{\mathbb{Z}}_2$. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a $\tau$-function of an integrable hierarchy.

36+24 pages, 4 figures; performed the matching with Liouville, improved discussion

References in corpus (14)

• A Perturbative Window into Non-Perturbative Physics
• String Cosmology: A Review
• The Annular Report on Non-Critical String Theory
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• The Black Hole S-Matrix from Quantum Mechanics
• From Big Crunch to Big Bang with AdS/CFT
• Matrix String Description of Cosmic Singularities in a Class of Time-dependent Solutions
• Non-singular string cosmology in a 2d Hybrid model
• Topological Matrix Models, Liouville Matrix Model and c=1 String Theory
• The Challenging Cosmic Singularity
• The Nothing at the Beginning of the Universe Made Precise
• Non-Unitary Holography
• A Note on the Pfaffian Integration Theorem
• Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals

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• Liouville theory and Matrix models: A Wheeler DeWitt perspective
• Black Hole S-matrix for a scalar field
• Microstates of a $2d$ Black Hole in string theory
• On the breakdown of the perturbative interaction picture in Big Crunch/Big Bang or the true reason why perturbative string amplitudes on temporal orbifolds diverge