1,142 research outputs found
Three Applications of Instanton Numbers
We use instanton numbers to: (i) stratify moduli of vector bundles, (ii)
calculate relative homology of moduli spaces and (iii) distinguish curve
singularities.Comment: To appear in Communications in Mathematical Physic
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
We address the nonperturbative structure of topological strings and c=1
matrix models, focusing on understanding the nature of instanton effects
alongside with exploring their relation to the large-order behavior of the 1/N
expansion. We consider the Gaussian, Penner and Chern-Simons matrix models,
together with their holographic duals, the c=1 minimal string at self-dual
radius and topological string theory on the resolved conifold. We employ Borel
analysis to obtain the exact all-loop multi-instanton corrections to the free
energies of the aforementioned models, and show that the leading poles in the
Borel plane control the large-order behavior of perturbation theory. We
understand the nonperturbative effects in terms of the Schwinger effect and
provide a semiclassical picture in terms of eigenvalue tunneling between
critical points of the multi-sheeted matrix model effective potentials. In
particular, we relate instantons to Stokes phenomena via a hyperasymptotic
analysis, providing a smoothing of the nonperturbative ambiguity. Our
predictions for the multi-instanton expansions are confirmed within the
trans-series set-up, which in the double-scaling limit describes
nonperturbative corrections to the Toda equation. Finally, we provide a
spacetime realization of our nonperturbative corrections in terms of toric
D-brane instantons which, in the double-scaling limit, precisely match
D-instanton contributions to c=1 minimal strings.Comment: 71 pages, 14 figures, JHEP3.cls; v2: added refs, minor change
The Sen Limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to
IIb compactifications by taking a certain limit in complex structure moduli
space, introduced by A. Sen. The limit has been characterized on the basis of
SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable
version of the Sen limit. In this picture the elliptic Calabi-Yau splits into
two pieces, a P^1-bundle and a conic bundle, and the intersection yields the
IIb space-time. We get a precise match between F-theory and perturbative type
IIb. The correspondence is holographic, in the sense that physical quantities
seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as
expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds
to summing up the D(-1)-instanton corrections to the IIb theory.Comment: 41 pp, 1 figure, LaTe
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