Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The complete non-perturbative partition function of minimal superstring theory and JT supergravity

Dan Stefan Eniceicu, Chitraang Murdia, Andrii Torchylo

TL;DR

The paper delivers a complete non-perturbative partition function for the ungapped phase of the $\ N=1$ $(2,4k)$ minimal superstring with type 0B GSO projection, achieved by recasting a double-scaled unitary matrix integral into a convergent Fredholm-determinant expansion. It identifies fundamental string-theory objects as F-branes and anti-F-branes, shows the partition function arises from disk and annulus contributions of these branes, and provides a Hilbert-space formulation in terms of dressed free fermions, with the partition function expressed as a Fredholm determinant of a trace-class operator. The formalism extends to the $k\to\infty$ limit, yielding exact non-perturbative JT supergravity, and yields closed expressions for $n$-point correlators of the eigenvalue density, interpreted as sums over brane-diagram sectors. Together with the operator- and momentum-space representations, these results offer a direct, non-perturbative handle on minimal superstring theory and its JT gravity limit, bypassing resurgence or differential-string equations in favor of a Fredholm-determinant framework. The work also invites extensions to other matrix-model duals and to direct gravitational derivations of the JT limit, enriching the bridge between non-perturbative string theory and quantum gravity.

Abstract

We derive an exact convergent expression for the partition function of the $\mathcal{N}=1$ $(2,4k)$ minimal superstring theory with type 0B GSO projection in the ungapped phase by leveraging the duality between this theory and a double-scaled unitary matrix integral. Taking the $k\rightarrow\infty$ limit, we also obtain the complete partition function of $\mathcal{N}=1$ JT supergravity, including all contributions associated with "doubly non-perturbative" effects. We discover that the fundamental objects of the string theory are a linear combination of the standard FZZT branes which we call F-branes, along with their charge-conjugate partners which we call anti-F-branes. Summing over the disk and cylinder diagram contributions of the F-branes and anti-F-branes and integrating over their moduli space completely reproduces our expression for the partition function from the matrix integral side of the duality. We show that the string theory can be expressed precisely in the formalism of dressed free fermions and we propose a Hilbert space interpretation of our results. We present exact expressions for the matrix integral correlators of the double-scaled eigenvalue density.

The complete non-perturbative partition function of minimal superstring theory and JT supergravity

TL;DR

The paper delivers a complete non-perturbative partition function for the ungapped phase of the minimal superstring with type 0B GSO projection, achieved by recasting a double-scaled unitary matrix integral into a convergent Fredholm-determinant expansion. It identifies fundamental string-theory objects as F-branes and anti-F-branes, shows the partition function arises from disk and annulus contributions of these branes, and provides a Hilbert-space formulation in terms of dressed free fermions, with the partition function expressed as a Fredholm determinant of a trace-class operator. The formalism extends to the limit, yielding exact non-perturbative JT supergravity, and yields closed expressions for -point correlators of the eigenvalue density, interpreted as sums over brane-diagram sectors. Together with the operator- and momentum-space representations, these results offer a direct, non-perturbative handle on minimal superstring theory and its JT gravity limit, bypassing resurgence or differential-string equations in favor of a Fredholm-determinant framework. The work also invites extensions to other matrix-model duals and to direct gravitational derivations of the JT limit, enriching the bridge between non-perturbative string theory and quantum gravity.

Abstract

We derive an exact convergent expression for the partition function of the minimal superstring theory with type 0B GSO projection in the ungapped phase by leveraging the duality between this theory and a double-scaled unitary matrix integral. Taking the limit, we also obtain the complete partition function of JT supergravity, including all contributions associated with "doubly non-perturbative" effects. We discover that the fundamental objects of the string theory are a linear combination of the standard FZZT branes which we call F-branes, along with their charge-conjugate partners which we call anti-F-branes. Summing over the disk and cylinder diagram contributions of the F-branes and anti-F-branes and integrating over their moduli space completely reproduces our expression for the partition function from the matrix integral side of the duality. We show that the string theory can be expressed precisely in the formalism of dressed free fermions and we propose a Hilbert space interpretation of our results. We present exact expressions for the matrix integral correlators of the double-scaled eigenvalue density.

Paper Structure

This paper contains 27 sections, 236 equations, 1 figure.

Table of Contents

  1. Introduction and summary
  2. The derivation of the partition function
  3. The double-scaling limit of the unitary matrix integral
  4. The minimal superstring theory partition function
  5. Properties of the partition function
  6. Properties of the expansion terms
  7. The expansion terms as disconnected diagrams
  8. The momentum space representation of the expansion terms
  9. The Hilbert space formulation
  10. Double-scaling at the operator level
  11. The partition function as a Fredholm determinant
  12. The minimal superstring as a theory of free fermions
  13. The dressed fermions
  14. The partition function as a trace
  15. Correlators of the eigenvalue density
  16. ...and 12 more sections

Figures (1)

  • Figure 1: Numerical results for $D_{1|1}(\kappa)$, the connected diagram involving one particle and one antiparticle, evaluated at $\kappa=0.1$. The $(2,4k)$ minimal superstring theory results as well as the JT supergravity limit are shown.