57 research outputs found
Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
The Stokes multipliers in the matrix models are invariants in the
string-theory moduli space and related to the D-instanton chemical potentials.
They not only represent non-perturbative information but also play an important
role in connecting various perturbative string theories in the moduli space.
They are a key concept to the non-perturbative completion of string theory and
also expected to imply some remnant of strong coupling dynamics in M theory. In
this paper, we investigate the non-perturbative completion problem consisting
of two constraints on the Stokes multipliers. As the first constraint, Stokes
phenomena which realize the multi-cut geometry are studied in the Z_k symmetric
critical points of the multi-cut two-matrix models. Sequence of solutions to
the constraints are obtained in general k-cut critical points. A discrete set
of solutions and a continuum set of solutions are explicitly shown, and they
can be classified by several constrained configurations of the Young diagram.
As the second constraint, we discuss non-perturbative stability of backgrounds
in terms of the Riemann-Hilbert problem. In particular, our procedure in the
2-cut (1,2) case (pure-supergravity case) completely fixes the D-instanton
chemical potentials and results in the Hastings-McLeod solution to the
Painlev\'e II equation. It is also stressed that the Riemann-Hilbert approach
realizes an off-shell background independent formulation of non-critical string
theory.Comment: 71 pages, v3: organization of Sec. 3, Sec. 4, App. C and App. D
improved, final version to be published in Nucl. Phys.
Duality Constraints on String Theory: Instantons and spectral networks
We study an implication of duality (spectral duality or T-duality) on
non-perturbative completion of minimal string theory. According to the
Eynard-Orantin topological recursion, spectral duality was already
checked for all-order perturbative analysis including instanton/soliton
amplitudes. Non-perturbative realization of this duality, on the other hand,
causes a new fundamental issue. In fact, we find that not all the
non-perturbative completions are consistent with non-perturbative
duality; Non-perturbative duality rather provides a constraint on
non-perturbative contour ambiguity (equivalently, of D-instanton fugacity) in
matrix models. In particular, it prohibits some of meta-stability caused by
ghost D-instantons, since there is no non-perturbative realization on the dual
side in the matrix-model description. Our result is the first quantitative
observation that a missing piece of our understanding in non-perturbative
string theory is provided by the principle of non-perturbative string duality.
To this end, we study Stokes phenomena of minimal strings with spectral
networks and improve the Deift-Zhou's method to describe meta-stable vacua. By
analyzing the instanton profile on spectral networks, we argue the duality
constraints on string theory.Comment: v1: 84 pages, 43 figures; v2: 86 pages, 43 figures, presentations are
improved, references added; v3: 126 pages, 69 figures: a solution of local
RHP, physics of resolvents, commutativity of integrals are newly added;
organization is changed and explanations are expanded to improve
representation with addition of review, proofs and calculations; some
definitions are changed; references adde
Wronskians, dualities and FZZT-Cardy branes
The resolvent operator plays a central role in matrix models. For instance,
with utilizing the loop equation, all of the perturbative amplitudes including
correlators, the free-energy and those of instanton corrections can be obtained
from the spectral curve of the resolvent operator. However, at the level of
non-perturbative completion, the resolvent operator is generally not sufficient
to recover all the information from the loop equations. Therefore it is
necessary to find a sufficient set of operators which provide the missing
non-perturbative information. In this paper, we study generalized Wronskians of
the Baker-Akhiezer systems as a manifestation of these new degrees of freedom.
In particular, we derive their isomonodromy systems and then extend several
spectral dualities to these systems. In addition, we discuss how these
Wronskian operators are naturally aligned on the Kac table. Since they are
consistent with the Seiberg-Shih relation, we propose that these new degrees of
freedom can be identified as FZZT-Cardy branes in Liouville theory. This means
that FZZT-Cardy branes are the bound states of elemental FZZT branes (i.e. the
twisted fermions) rather than the bound states of principal FZZT-brane (i.e.
the resolvent operator).Comment: 131 pages, 4 figure
Analytic Study for the String Theory Landscapes via Matrix Models
We demonstrate a first-principle analysis of the string theory landscapes in
the framework of non-critical string/matrix models. In particular, we discuss
non-perturbative instability, decay rate and the true vacuum of perturbative
string theories. As a simple example, we argue that the perturbative string
vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is
inescapably a false vacuum. Surprisingly, most of perturbative minimal string
vacua are unstable, and their true vacuum mostly does not suffer from
non-perturbative ambiguity. Importantly, we observe that the instability of
these tachyon-less closed string theories is caused by ghost D-instantons (or
ghost ZZ-branes), the existence of which is determined only by non-perturbative
completion of string theory.Comment: v1: 5 pages, 2 figures; v2: references and footnote added; v3: 7
pages, 4 figures, organization changed, explanations expanded, references
added, reconstruction program from arbitrary spectral curves shown explicitl
Three-dimensional imaging of crack growth in L chondrites after high-velocity impact experiments
Small asteroids such as Itokawa are covered with an unconsolidated regolith layer of centimeter-sized or smaller particles. There are two plausible formation mechanisms for regolith layers on a sub-kilometer-sized asteroid: (i) fragments produced by thermal fatigue by day-night temperature cycles on the asteroid surface and (ii) impact fragment. Previous studies suggest that thermal fatigue induces crack growth along the boundary surface of the mineral grain while impact phenomena may induce crack growth regardless of the boundary surface of the mineral grain. Therefore, it is possible that the crack growth within a mineral grain (and/or a chondrule) differs depending on the crack formation mechanism, be it thermal fatigue or an impact. In order to investigate how mineral grains and chondrules are affected by impact-induced crack growth, we fired spherical alumina projectiles (diameter ~1 mm) into 9 mm side length cubic targets of L chondrites at a nominal impact velocity of 2.0 km/s. Before and after the six successful impact experiments, the cracks within mineral grains and chondrules in the respective targets are examined using X-ray microtomography at a resolution with the voxel size of 9.0 μm. The results show that most cracks within chondrules and troilite (FeS) grow regardless of the boundary surfaces of the grains while most cracks within ductile Fe-Ni metal grow along the boundary surfaces of the grains. This may indicate that crack growth is largely affected by the strength of mineral grains (and/or chondrules). From the experimental results and the fact that the shapes of polymineralic and monomineralic particles from Itokawa are similar, we conclude that the Itokawa particles have not been produced by thermal fatigue but instead are likely to be impact fragments, as described in previous papers (Tsuchiyama et al., 2011, 2014; Michikami et al., 2018)
Macroscopic loop amplitudes in the multi-cut two-matrix models
Multi-cut critical points and their macroscopic loop amplitudes are studied
in the multi-cut two-matrix models, based on an extension of the prescription
developed by Daul, Kazakov and Kostov. After identifying possible critical
points and potentials in the multi-cut matrix models, we calculate the
macroscopic loop amplitudes in the Z_k symmetric background. With a natural
large N ansatz for the matrix Lax operators, a sequence of new solutions for
the amplitudes in the Z_k symmetric k-cut two-matrix models are obtained, which
are realized by the Jacobi polynomials.Comment: 46 pages, 3 figures; v2: 51 pages, 7 figures, notations changed,
explanations in Section 2.4 extended, figures for topology of the curves
added, Appendix E added, final version to appear in Nucl. Phys.
Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
Multi-cut two-matrix models are studied in the Z_k symmetry breaking k-cut
(\hat p,\hat q) critical points which should correspond to (\hat p,\hat q)
minimal k-fractional superstring theory. FZZT-brane or macroscopic loop
amplitudes are obtained in all of these critical points and found to have two
kinds of solutions in general. Each of these solutions is expressed by
hyperbolic cosine or sine functions with proper phase shifts. The algebraic
geometries and ZZ-brane disk amplitudes (instanton actions) of these solutions
are also studied. In particular, our results suggest that minimal
\infty-fractional superstring theory can be viewed as a mother theory which
includes all the minimal k-fractional superstring theories (k=1,2,...) as its
perturbative vacua in the weak-coupling string landscape. Our results also
indicate that, in the strong coupling regime of this fractional superstring
theory, there is a three-dimensional theory which would be understood as the
non-critical version of M theory in the sense proposed by P. Horava and C. A.
Keeler.Comment: 47 pages, 6 figures; references added v
- …