25,496 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
The Topology of Dislocations in Smectic Liquid Crystals
The order parameter of the smectic liquid crystal phase is the same as that
of a superfluid or superconductor, namely a complex scalar field. We show that
the essential difference in boundary conditions between these systems leads to
a markedly different topological structure of the defects. Screw and edge
defects can be distinguished topologically. This implies an invariant on an
edge dislocation loop so that smectic defects can be topologically linked not
unlike defects in ordered systems with non-Abelian fundamental groups.Comment: 11 pages, many figures, the full catastrophe. Supplementary data with
two movies can be found at
http://iopscience.iop.org/article/10.1088/1367-2630/18/5/05301
Topological changes of two-dimensional magnetic textures
We investigate the interaction of magnetic vortices and skyrmions with a
spin-polarized current. In a square lattice, fixed classical spins and quantum
itinerant electrons, evolve according to the coupled Landau-Lifshitz and
Schr\"odinger equations. Changes in the topology occur at microscopic time and
length scales, and are shown to be triggered by the nucleation of a nontrivial
electron-spin structure at the vortex core.Comment: See supplementary material (high resolution figures and movies)
https://drive.google.com/folderview?id=0By4j_RJ9SKLpQ2R5UklXLURvbEE&usp=sharing
--- v2: Extended versio
Tropical polar cones, hypergraph transversals, and mean payoff games
We discuss the tropical analogues of several basic questions of convex
duality. In particular, the polar of a tropical polyhedral cone represents the
set of linear inequalities that its elements satisfy. We characterize the
extreme rays of the polar in terms of certain minimal set covers which may be
thought of as weighted generalizations of minimal transversals in hypergraphs.
We also give a tropical analogue of Farkas lemma, which allows one to check
whether a linear inequality is implied by a finite family of linear
inequalities. Here, the certificate is a strategy of a mean payoff game. We
discuss examples, showing that the number of extreme rays of the polar of the
tropical cyclic polyhedral cone is polynomially bounded, and that there is no
unique minimal system of inequalities defining a given tropical polyhedral
cone.Comment: 27 pages, 6 figures, revised versio
Experimental Evidence on English Auctions: Oral Outcry vs. Clock
This paper tests experimentally, in a common value setting, the equivalence between the Japanese English auction (or clock auction) and an open outcry auction, where bidders are allowed to call their own bids. We find that (i) bidding behaviour is different in each type of auction, but also that (ii) this difference in bidding behaviour does not affect significantly the auction prices. This lends some support to the equivalence between these two types of auction. The winner's curse is present: overbidding led to higher than expected prices (under Nash bidding strategies) in both types of auction.English auctions, discrete bidding, winner's curse
Black holes and the double copy
Recently, a perturbative duality between gauge and gravity theories (the
double copy) has been discovered, that is believed to hold to all loop orders.
In this paper, we examine the relationship between classical solutions of
non-Abelian gauge theory and gravity. We propose a general class of gauge
theory solutions that double copy to gravity, namely those involving stationary
Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their
higher-dimensional equivalents) emerge as special cases. We also discuss plane
wave solutions. Furthermore, a recently examined double copy between the
self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a
momentum-space generalisation of the Kerr-Schild framework.Comment: 22 pages; typos corrected and references adde
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