Exact vs. semiclassical target space of the minimal string

By J. Maldacena, G. Moore, N. Seiberg, David Shih. 2004

185 citations recorded by the source corpus.

We study both the classical and the quantum target space of (p,q) minimal string theory, using the FZZT brane as a probe. By thinking of the target space as the moduli space of FZZT branes, parametrized by the boundary cosmological constant x, we see that classically it consists of a Riemann surface p,q which is a p-sheeted cover of the complex x plane. However, we show using the dual matrix model that the exact quantum FZZT observables exhibit Stokes' phenomenon and are entire functions of x. Along the way we clarify some points about the semiclassical limit of D-brane correlation functions. The upshot is that nonperturbative effects modify the target space drastically, changing it from p,q to the complex x plane. To illustrate these ideas, we study in detail the example of (p,q) = (2,1), which is dual to the gaussian matrix model. Here we learn that the other sheets of the classical Riemann surface describe instantons in the effective theory on the brane. Finally, we discuss possible applications to black holes and the topological string.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1fafd132f304890354f17a9f25c876004ba4c6cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. E. Witten
2. Marcos Mariño
3. Phil Saad
4. S. Shenker
5. D. Stanford
6. Mina Aganagic
7. C. Vafa
8. Sergei Gukov

In Nuclear and High Energy Physics

1. Phil Saad
2. D. Stanford
3. S. Shenker
4. E. Witten
5. J. Maldacena
6. D. Harlow
7. Jordan S. Cotler
8. K. Jensen

In Statistical and Nonlinear Physics

1. Phil Saad
2. D. Stanford
3. S. Shenker
4. E. Witten
5. J. Maldacena
6. Jordan S. Cotler
7. K. Jensen
8. G. Turiaci

Citations in the corpus

• Open string amplitudes and large order behavior in topological string theory (2006, background): “is nothing but the Laplace transform of the macroscopic loop operator of 2d gravity [34, 25], and it corresponds to the disk amplitude of the FZZT brane of Liouville theory (see [67, 52] and references therein).”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “The rules for including D-brane boundaries do not have a clear origin in gravity; we must rely upon the matrix integral description of JT gravity to understand how to properly (31)These branes are also closely related to branes in topological string theories described by matrix models [64, 65, 66, 6”
• Large N BPS states and emergent quantum gravity (2005, unknown): “See for example [27, 28] and references therein”
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, background): “s. We interpret the sum over multi-instantons that arises naturally in the trans-series solution as a sum over ZZ brane backgrounds, i.e. over sub-leading saddles of the theory. It was pointed out in [61] that the exact, nonperturbative answer for the free energy in noncritical string theories shoul”
• JT gravity and the ensembles of random matrix theory (2019, background): “As explained in [108], one has to sum over branch choices for Ψ(x) with the right coefficients.”
• JT gravity as a matrix integral (2019, background): “This (2g)! behavior is generic in string theory [44] and the e−1/gs nonperturbative effects it points to are due to D-branes [46].”
• Analytic Continuation Of Chern-Simons Theory (2010, unknown): “Various aspects of this framework have been applied to quantum field theory from different points of view [41–45].”