128 research outputs found
Dimer Models from Mirror Symmetry and Quivering Amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to
encode the gauge groups, matter content and tree-level superpotential of the
world-volume quiver gauge theories obtained by placing D3-branes at the tip of
a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the
quiver graph. However, the string theoretic explanation of this was unclear. In
this paper we use mirror symmetry to shed light on this: the dimer models live
on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is
wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the
singular point, and geometrically encode the same quiver theory on their
world-volume.Comment: 55 pages, 27 figures, LaTeX2
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Dimer models from mirror symmetry and quivering amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume
The String Landscape, the Swampland, and the Missing Corner
We give a brief overview of the string landscape and techniques used to
construct string compactifications. We then explain how this motivates the
notion of the swampland and review a number of conjectures that attempt to
characterize theories in the swampland. We also compare holography in the
context of superstrings with the similar, but much simpler case of topological
string theory. For topological strings, there is a direct definition of
topological gravity based on a sum over a "quantum gravitational foam." In this
context, holography is the statement of an identification between a gravity and
gauge theory, both of which are defined independently of one another. This
points to a missing corner in string dualities which suggests the search for a
direct definition of quantum theory of gravity rather than relying on its
strongly coupled holographic dual as an adequate substitute (Based on TASI 2017
lectures given by C. Vafa)
Brane Tilings and Their Applications
We review recent developments in the theory of brane tilings and
four-dimensional N=1 supersymmetric quiver gauge theories. This review consists
of two parts. In part I, we describe foundations of brane tilings, emphasizing
the physical interpretation of brane tilings as fivebrane systems. In part II,
we discuss application of brane tilings to AdS/CFT correspondence and
homological mirror symmetry. More topics, such as orientifold of brane tilings,
phenomenological model building, similarities with BPS solitons in
supersymmetric gauge theories, are also briefly discussed.
This paper is a revised version of the author's master's thesis submitted to
Department of Physics, Faculty of Science, the University of Tokyo on January
2008, and is based on his several papers: math.AG/0605780, math.AG/0606548,
hep-th/0702049, math.AG/0703267, arXiv:0801.3528 and some works in progress.Comment: 208 pages, 92 figures, based on master's thesis; v2: minor
corrections, to appear in Fortschr. Phy
Experimental determination of the magnetic interactions of frustrated Cairo pentagon lattice materials
We present inelastic neutron scattering measurements of the Cairo pentagon
lattice magnets BiFeO and BiFeOF, supported by high
field magnetisation measurements of BiFeO. Using linear spin wave
theory and mean field analyses we determine the spin exchange interactions and
single-ion anisotropy in these materials. The Cairo lattice is geometrically
frustrated and consists of two inequivalent magnetic sites, both occupied by
Fe ions and connected by two competing nearest neighbour interactions.
We found that one of these interactions, coupling nearest neighbour spins on
the three-fold symmetric sites, is extremely strong and antiferromagnetic.
These strongly coupled dimers are then weakly coupled to a framework formed
from spins occupying the other inequivalent site. In addition we found that the
Fe spins have a non-negligible single-ion anisotropy, which
manifests as a spin anisotropy gap in the neutron spectrum and a spin-flop
transition in high field magnetisation measurements.Comment: 10 pages, 9 figure
Duality and dynamics of supersymmetric field theories from D-branes on singularities
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (p. 359-373).We carry out various investigations regarding gauge theories on the worldvolume of D-branes probing toric singularities. We first study the connection that arises in Toric Duality between different dual gauge theory phases and the multiplicity of fields in the gauged linear sigma models associated with the probed geometries. We introduce a straightforward procedure for the determination of toric dual theories and partial resolutions based on the (p, q) web description of toric singularities. We study the non-conformal theories that arise in the presence of fractional branes. We introduce a systematic procedure to study the resulting cascading RG flows, including the effect of anomalous dimensions on beta functions. Supergravity solutions dual to logarithmic RG flows are constructed, validating the field theory analysis of the cascades. We systematically study the IR dynamics of cascading gauge theories. We show how the deformation in the dual geometries is encoded in a quantum modification of the moduli space. We construct an infinite family of superconformal quiver gauge theories which are AdS/CFT dual to Sasaki-Einstein horizons with explicit metrics. The gauge theory and geometric computations of R-charges and central charges are shown to agree. We introduce new Type IIB brane constructions denoted brane tilings which are dual to D3-branes probing arbitrary toric singularities. Brane tilings encode both the quiver and superpotential of the gauge theories on the D-brane probes. They give a connection with the statistical model of dimers.(cont.) They provide the simplest known method for computing toric moduli spaces of gauge theories, which reduces to finding the determinant of the Kasteleyn matrix of a bipartite graph.by Sebastián Federico Franco.Ph.D
クラスS理論における欠陥演算子への幾何学的アプローチ
学位の種別: 課程博士審査委員会委員 : (主査)東京大学准教授 松尾 泰, 東京大学教授 浅井 祥仁, 東京大学教授 国場 敦夫, 東京大学准教授 渡利 泰山, 東京大学教授 押川 正毅University of Tokyo(東京大学
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