3,427 research outputs found
Calabi-Yau threefolds with large h^{2, 1}
We carry out a systematic analysis of Calabi-Yau threefolds that are
elliptically fibered with section ("EFS") and have a large Hodge number h^{2,
1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of
moduli space associated with different topologies connected through transitions
that can be understood in terms of singular Weierstrass models. We determine
the complete set of such threefolds that have h^{2, 1} >= 350 by tuning
coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set
of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2,
1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate
that there are no other Calabi-Yau threefolds (elliptically fibered or not)
with Hodge numbers that exceed this bound. We summarize the theoretical and
practical obstacles to a complete enumeration of all possible EFS Calabi-Yau
threefolds and fourfolds, including those with small Hodge numbers, using this
approach.Comment: 44 pages, 5 tables, 5 figures; v2: minor corrections; v3: minor
corrections, moved figure; v4: typo in Table 2 correcte
Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
The two-dimensional supersymmetric gauged linear sigma model (GLSM) with
abelian gauge groups and matter fields has provided many insights into string
theory on Calabi--Yau manifolds of a certain type: complete intersections in
toric varieties. In this paper, we consider two GLSM constructions with
nonabelian gauge groups and charged matter whose infrared CFTs correspond to
string propagation on determinantal Calabi-Yau varieties, furnishing another
broad class of Calabi-Yau geometries in addition to complete intersections. We
show that these two models -- which we refer to as the PAX and the PAXY model
-- are dual descriptions of the same low-energy physics. Using GLSM techniques,
we determine the quantum K\"ahler moduli space of these varieties and find no
disagreement with existing results in the literature.Comment: v3: 46 pages, 1 figure. Corrected phase structure of general linear
determinantal varieties. Typos correcte
Structure in 6D and 4D N=1 supergravity theories from F-theory
We explore some aspects of 4D supergravity theories and F-theory vacua that
are parallel to structures in the space of 6D theories. The spectrum and
topological terms in 4D supergravity theories correspond to topological data of
F-theory geometry, just as in six dimensions. In particular, topological
axion-curvature squared couplings appear in 4D theories; these couplings are
characterized by vectors in the dual to the lattice of axion shift symmetries
associated with string charges. These terms are analogous to the Green-Schwarz
terms of 6D supergravity theories, though in 4D the terms are not generally
linked with anomalies. We outline the correspondence between F-theory topology
and data of the corresponding 4D supergravity theories. The correspondence of
geometry with structure in the low-energy action illuminates topological
aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of
an F-theory realization also places geometrical constraints on the 4D
supergravity theory in the large-volume limit.Comment: 63 page
6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
We carry out a systematic study of a class of 6D F-theory models and
associated Calabi-Yau threefolds that are constructed using base surfaces with
a generalization of toric structure. In particular, we determine all smooth
surfaces with a structure invariant under a single C^* action (sometimes called
"T-varieties" in the mathematical literature) that can act as bases for an
elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404
distinct bases, which include as a subset the previously studied set of
strictly toric bases. Calabi-Yau threefolds constructed in this fashion include
examples with previously unknown Hodge numbers. There are also bases over which
the generic elliptic fibration has a Mordell-Weil group of sections with
nonzero rank, corresponding to non-Higgsable U(1) factors in the 6D
supergravity model; this type of structure does not arise for generic elliptic
fibrations in the purely toric context.Comment: 38 pages, 17 figures; v2: references added, minor typos corrected;
v3: additional constraints rule out 4 inconsistent bases, minor cosmetic
improvements; v4:minor clarifications, typo correcte
Nonabelian Confinement near Nontrivial Conformal Vacua
We discuss some aspects of confinement and dynamical symmetry breaking in the
so-called nonabelian Argyres-Douglas vacua, which occur very generally in
supersymmetric theories. These systems are characterized by strongly-coupled
nonabelian monopoles and dyons; confinement and dynamical symmetry breaking are
caused by the condensation of monopole composites, rather than by condensation
of single weakly-coupled monopoles. In general, there are strong constraints on
which kind of monopoles can appear as the infrared degrees of freedom, related
to the proper realization of the global symmetry of the theory. Drawing
analogies to some of the phenomena found here, we make a speculation on the
ground state of the standard QCD.Comment: 28 pages, Late
Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
The Pfaffian quantum Hall states, which can be viewed as involving pairing
either of spin-polarized electrons or of composite fermions, are generalized by
finding the exact ground states of certain Hamiltonians with k+1-body
interactions, for all integers k > 0. The remarkably simple wavefunctions of
these states involve clusters of k particles, and are related to correlators of
parafermion currents in two-dimensional conformal field theory. The k=2 case is
the Pfaffian. For k > 1, the quasiparticle excitations of these systems are
expected to possess nonabelian statistics, like those of the Pfaffian. For k=3,
these ground states have large overlaps with the ground states of the (2-body)
Coulomb-interaction Hamiltonian for electrons in the first excited Landau level
at total filling factors \nu=2+3/5, 2+2/5.Comment: 11 pages Revtex in two column format with 4 eps figures included in
the M
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