9,668 research outputs found
Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
The holomorphic anomaly equations describe B-model closed topological strings
in Calabi-Yau geometries. Having been used to construct perturbative
expansions, it was recently shown that they can also be extended past
perturbation theory by making use of resurgent transseries. These yield formal
nonperturbative solutions, showing integrability of the holomorphic anomaly
equations at the nonperturbative level. This paper takes such constructions one
step further by working out in great detail the specific example of topological
strings in the mirror of the local CP2 toric Calabi-Yau background, and by
addressing the associated (resurgent) large-order analysis of both perturbative
and multi-instanton sectors. In particular, analyzing the asymptotic growth of
the perturbative free energies, one finds contributions from three different
instanton actions related by Z_3 symmetry, alongside another action related to
the Kahler parameter. Resurgent transseries methods then compute, from the
extended holomorphic anomaly equations, higher instanton sectors and it is
shown that these precisely control the asymptotic behavior of the perturbative
free energies, as dictated by resurgence. The asymptotic large-order growth of
the one-instanton sector unveils the presence of resonance, i.e., each
instanton action is necessarily joined by its symmetric contribution. The
structure of different resurgence relations is extensively checked at the
numerical level, both in the holomorphic limit and in the general
nonholomorphic case, always showing excellent agreement with transseries data
computed out of the nonperturbative holomorphic anomaly equations. The
resurgence relations further imply that the string free energy displays an
intricate multi-branched Borel structure, and that resonance must be properly
taken into account in order to describe the full transseries solution.Comment: 63 pages, 54 images in 24 figures, jheppub-nosort.sty; v2: corrected
figure, minor changes, final version for CM
Resurgent Transseries and the Holomorphic Anomaly
The gauge theoretic large N expansion yields an asymptotic series which
requires a nonperturbative completion in order to be well defined. Recently,
within the context of random matrix models, it was shown how to build resurgent
transseries solutions encoding the full nonperturbative information beyond the
't Hooft genus expansion. On the other hand, via large N duality, random matrix
models may be holographically described by B-model closed topological strings
in local Calabi-Yau geometries. This raises the question of constructing the
corresponding holographically dual resurgent transseries, tantamount to
nonperturbative topological string theory. This paper addresses this point by
showing how to construct resurgent transseries solutions to the holomorphic
anomaly equations. These solutions are built upon (generalized) multi-instanton
sectors, where the instanton actions are holomorphic. The asymptotic expansions
around the multi-instanton sectors have both holomorphic and anti-holomorphic
dependence, may allow for resonance, and their structure is completely fixed by
the holomorphic anomaly equations in terms of specific polynomials multiplied
by exponential factors and up to the holomorphic ambiguities -- which
generalizes the known perturbative structure to the full transseries. In
particular, the anti-holomorphic dependence has a somewhat universal character.
Furthermore, in the nonperturbative sectors, holomorphic ambiguities may be
fixed at conifold points. This construction shows the nonperturbative
integrability of the holomorphic anomaly equations, and sets the ground to
start addressing large-order analysis and resurgent nonperturbative completions
within closed topological string theory.Comment: 59 pages, jheppub-nosort.sty; v2: small additions, minor changes,
refs updated; v3: more minor corrections, final version for AH
Cubic Time Recognition of Cocircuit Graphs of Uniform Oriented Matroids
We present an algorithm which takes a graph as input and decides in cubic
time if the graph is the cocircuit graph of a uniform oriented matroid. In the
affirmative case the algorithm returns the set of signed cocircuits of the
oriented matroid. This improves an algorithm proposed by Babson, Finschi and
Fukuda.
Moreover we strengthen a result of Montellano-Ballesteros and Strausz about
crabbed connectivity of cocircuit graphs of uniform oriented matroids.Comment: 9 page
Exponential wealth distribution in a random market. A rigorous explanation
In simulations of some economic gas-like models, the asymptotic regime shows
an exponential wealth distribution, independently of the initial wealth
distribution given to the system. The appearance of this statistical
equilibrium for this type of gas-like models is explained in a rigorous
analytical way.Comment: 9 pages, 4 figure
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