543 research outputs found
Supereigenvalue Models and Topological Recursion
We show that the Eynard-Orantin topological recursion, in conjunction with
simple auxiliary equations, can be used to calculate all correlation functions
of supereigenvalue models.Comment: 46 pages. v2: published version (minor changes to the presentation
Reconstructing WKB from topological recursion
We prove that the topological recursion reconstructs the WKB expansion of a
quantum curve for all spectral curves whose Newton polygons have no interior
point (and that are smooth as affine curves). This includes nearly all
previously known cases in the literature, and many more; in particular, it
includes many quantum curves of order greater than two. We also explore the
connection between the choice of ordering in the quantization of the spectral
curve and the choice of integration divisor to reconstruct the WKB expansion.Comment: 68 pages, 9 figures. v2: published version (improved presentation
Topological recursion and mirror curves
We study the constant contributions to the free energies obtained through the
topological recursion applied to the complex curves mirror to toric Calabi-Yau
threefolds. We show that the recursion reproduces precisely the corresponding
Gromov-Witten invariants, which can be encoded in powers of the MacMahon
function. As a result, we extend the scope of the "remodeling conjecture" to
the full free energies, including the constant contributions. In the process we
study how the pair of pants decomposition of the mirror curves plays an
important role in the topological recursion. We also show that the free
energies are not, strictly speaking, symplectic invariants, and that the
recursive construction of the free energies does not commute with certain
limits of mirror curves.Comment: 37 pages, 4 figure
On heterotic model constraints
The constraints imposed on heterotic compactifications by global consistency
and phenomenology seem to be very finely balanced. We show that weakening these
constraints, as was proposed in some recent works, is likely to lead to
frivolous results. In particular, we construct an infinite set of such
frivolous models having precisely the massless spectrum of the MSSM and other
quasi-realistic features. Only one model in this infinite collection (the one
constructed in arXiv:hep-th/0512149) is globally consistent and supersymmetric.
The others might be interpreted as being anomalous, or as non-supersymmetric
models, or as local models that cannot be embedded in a global one. We also
show that the strongly coupled model of arXiv:hep-th/0512149 can be modified to
a perturbative solution with stable SU(4) or SU(5) bundles in the hidden
sector. We finally propose a detailed exploration of heterotic vacua involving
bundles on Calabi-Yau threefolds with Z_6 Wilson lines; we obtain many more
frivolous solutions, but none that are globally consistent and supersymmetric
at the string scale.Comment: 38 page
Think globally, compute locally
We introduce a new formulation of the so-called topological recursion, that
is defined globally on a compact Riemann surface. We prove that it is
equivalent to the generalized recursion for spectral curves with arbitrary
ramification. Using this global formulation, we also prove that the correlation
functions constructed from the recursion for curves with arbitrary ramification
can be obtained as suitable limits of correlation functions for curves with
only simple ramification. It then follows that they both satisfy the properties
that were originally proved only for curves with simple ramification.Comment: 37 pages, v2: published versio
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