324 research outputs found
Phase transitions, double-scaling limit, and topological strings
Topological strings on Calabi--Yau manifolds are known to undergo phase
transitions at small distances. We study this issue in the case of perturbative
topological strings on local Calabi--Yau threefolds given by a bundle over a
two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory,
and it has a conjectural nonperturbative description in terms of q--deformed 2d
Yang--Mills theory. We solve the planar model and find a phase transition at
small radius in the universality class of 2d gravity. We give strong evidence
that there is a double--scaled theory at the critical point whose all genus
free energy is governed by the Painlev\'e I equation. We compare the critical
behavior of the perturbative theory to the critical behavior of its
nonperturbative description, which belongs to the universality class of 2d
supergravity. We also give evidence for a new open/closed duality relating
these Calabi--Yau backgrounds to open strings with framing.Comment: 49 pages, 3 eps figures; section added on non-perturbative proposal
and 2d gravity; minor typos correcte
Transition to Chaotic Phase Synchronization through Random Phase Jumps
Phase synchronization is shown to occur between opposite cells of a ring
consisting of chaotic Lorenz oscillators coupled unidirectionally through
driving. As the coupling strength is diminished, full phase synchronization
cannot be achieved due to random generation of phase jumps. The brownian
dynamics underlying this process is studied in terms of a stochastic diffusion
model of a particle in a one-dimensional medium.Comment: Accepted for publication in IJBC, 10 pages, 5 jpg figure
Counting BPS states on the Enriques Calabi-Yau
We study topological string amplitudes for the FHSV model using various
techniques. This model has a type II realization involving a Calabi-Yau
threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By
applying heterotic/type IIA duality, we compute the topological amplitudes in
the fibre to all genera. It turns out that there are two different ways to do
the computation that lead to topological couplings with different BPS content.
One of them leads to the standard D0-D2 counting amplitudes, and from the other
one we obtain information about bound states of D0-D4-D2 branes on the Enriques
fibre. We also study the model using mirror symmetry and the holomorphic
anomaly equations. We verify in this way the heterotic results for the D0-D2
generating functional for low genera and find closed expressions for the
topological amplitudes on the total space in terms of modular forms, and up to
genus four. This model turns out to be much simpler than the generic B-model
and might be exactly solvable.Comment: 62 pages, v3: some results at genus 3 corrected, more typos correcte
ABJM theory as a Fermi gas
The partition function on the three-sphere of many supersymmetric
Chern-Simons-matter theories reduces, by localization, to a matrix model. We
develop a new method to study these models in the M-theory limit, but at all
orders in the 1/N expansion. The method is based on reformulating the matrix
model as the partition function of an ideal Fermi gas with a non-trivial,
one-particle quantum Hamiltonian. This new approach leads to a completely
elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver
Chern-Simons-matter theories. In addition, the full series of 1/N corrections
to the original matrix integral can be simply determined by a next-to-leading
calculation in the WKB or semiclassical expansion of the quantum gas, and we
show that, for several quiver Chern-Simons-matter theories, it is given by an
Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama
for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas
corresponds to a strong coupling expansion in type IIA theory, and it is dual
to the genus expansion. This allows us to calculate explicitly non-perturbative
effects due to D2-brane instantons in the AdS background.Comment: 52 pages, 11 figures. v3: references, corrections and clarifications
added, plus a footnote on the relation to the recent work by Hanada et a
Solving the Topological String on K3 Fibrations
We present solutions of the holomorphic anomaly equations for compact
two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted
projective space. In particular we focus on K3-fibrations where due to
heterotic type II duality the topological invariants in the fibre direction are
encoded in certain modular forms. The formalism employed provides holomorphic
expansions of topological string amplitudes everywhere in moduli space.Comment: 60 pages, 1 figure, With an appendix by Sheldon Kat
Wave-induced extreme water levels in the Puerto Morelos fringing reef lagoon
Wave-induced extreme water levels in the Puerto Morelos fringing reef lagoon are investigated by means of a phase-resolving non-hydrostatic wave model (SWASH). This model solves the nonlinear shallow water equations including non-hydrostatic pressure. The one-dimensional version of the model is implemented in order to investigate wave transformation in fringing reefs. Firstly, the numerical model is validated with (i) laboratory experiments conducted on a physical model (Demirbilek et al., 2007)and (ii) field observations (Coronado et al., 2007). Numerical results show good agreement with both experimental and field data. The comparison against the physical model results, for energetic wave conditions, indicates that high- and low-frequency wave transformation is well reproduced. Moreover, extreme water-level conditions measured during the passage of Hurricane Ivan in Puerto Morelos are also estimated by the numerical tool. Subsequently, the model is implemented at different along-reef locations in Puerto Morelos. Extreme water levels, wave-induced setup, and infragravity wave energy are estimated inside the reef lagoon for different storm wave conditions (<i>H</i><sub>s</sub> >2 m). The numerical results revealed a strong correlation between the offshore sea-swell wave energy and the setup. In contrast, infragravity waves are shown to be the result of a more complex pattern which heavily relies on the reef geometry. Indeed, the southern end of the reef lagoon provides evidence of resonance excitation, suggesting that the reef barrier may act as either a natural flood protection morphological feature, or as an inundation hazard enhancer depending on the incident wave conditions
Global Properties of Topological String Amplitudes and Orbifold Invariants
We derive topological string amplitudes on local Calabi-Yau manifolds in
terms of polynomials in finitely many generators of special functions. These
objects are defined globally in the moduli space and lead to a description of
mirror symmetry at any point in the moduli space. Holomorphic ambiguities of
the anomaly equations are fixed by global information obtained from boundary
conditions at few special divisors in the moduli space. As an illustration we
compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.Comment: 34 pages, 3 figure
Star Algebra Projectors
Surface states are open string field configurations which arise from Riemann
surfaces with a boundary and form a subalgebra of the star algebra. We find
that a general class of star algebra projectors arise from surface states where
the open string midpoint reaches the boundary of the surface. The projector
property of the state and the split nature of its wave-functional arise because
of a nontrivial feature of conformal maps of nearly degenerate surfaces.
Moreover, all such projectors are invariant under constant and opposite
translations of their half-strings. We show that the half-string states
associated to these projectors are themselves surface states. In addition to
the sliver, we identify other interesting projectors. These include a butterfly
state, which is the tensor product of half-string vacua, and a nothing state,
where the Riemann surface collapses.Comment: 65 pages, 23 figures, LaTe
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
In these lectures I give a pedagogical presentation of some of the recent
progress in supersymmetric Chern-Simons-matter theories, coming from the use of
localization and matrix model techniques. The goal is to provide a simple
derivation of the exact interpolating function for the free energy of ABJM
theory on the three-sphere, which implies in particular the N^{3/2} behavior at
strong coupling. I explain in detail part of the background needed to
understand this derivation, like holographic renormalization, localization of
path integrals, and large N techniques in matrix modelsComment: 73 pages, 7 figures. v2: references and clarifications added,
misprints corrected. v3: more references, clarifications, and corrections.
v4: more corrections and clarifications, final version to appear in J. Phys.
Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications
Non-perturbative corrections and modular properties of four-dimensional type
IIB Calabi-Yau orientifolds are discussed. It is shown that certain
non-perturbative alpha' corrections survive in the large volume limit of the
orientifold and periodically correct the Kahler potential. These corrections
depend on the NS-NS two form and have to be completed by D-instanton
contributions to transform covariantely under symmetries of the type IIB
orientifold background. It is shown that generically also the D-instanton
superpotential depends on the two-form moduli as well as on the complex
dilaton. These contributions can arise through theta-functions with the dilaton
as modular parameter. An orientifold of the Enriques Calabi-Yau allows to
illustrate these general considerations. It is shown that this compactification
leads to a controlled four-dimensional N=1 effective theory due to the absence
of various quantum corrections. Making contact to the underlying topological
string theory the D-instanton superpotential is proposed to be related to a
specific modular form counting D3, D1, D(-1) degeneracies on the Enriques
Calabi-Yau.Comment: 35 page
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