Brane tilings and their applications

Yamazaki, Masahito

doi:10.1002/prop.200810536

Cited by 126 publications

(165 citation statements)

References 348 publications

(568 reference statements)

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“…There has been a large amount of research on this in the past twenty years [125,126,127,128,129] and has recently been revived as a possible extension of the story of theories of class S [130,127,128,129].…”

Section: Pos(tasi2017)015mentioning

confidence: 99%

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The String Landscape, the Swampland, and the Missing Corner

Vafa¹,

Brennan²,

Carta³

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

142

209

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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). Theoretical Advanced Study Institute in Elementary PoS(TASI2017)015The String Landscape, the Swampland, and the Missing Corner Cumrun VafaThese lecture notes from TASI 2017 give a brief overview of some of the open problems in string theory. We will be generally motivated by the philosophy that string theory is ultimately supposed to describe the fundamental laws of our universe. String theory is so versatile that it can be used to study a wide array of physical problems such as various topics in condensed matter and quark-gluon plasma or aspects of quantum fields theories in diverse dimensions. Much of the recent work using string theory has been focused on using its properties to solve specific problems rather than developing our understanding of string theory as a fundamental description of our universe. Here we aim to discuss topics which we hope will be useful in bringing string theory closer to observable aspects of fundamental physics.With this philosophy in mind, we will begin these lectures by reviewing some of what we know about string theory and its possible application to the universe by describing some generalities about the space of low energy theories theories coming from string theory compactifications: this is called the "string landscape." Supersymmetry plays a key organizing principle in this context. This will naturally lead us to investigate the question of how we know a priori if a low energy theory is in the landscape or it is not. The set of low energy physics models which look consistent but ultimately are not when coupled to gravity, is called the "swampland." Finding simple criteria to distinguish the swampland from the landscape is of great importance. In particular such criteria can lead to concrete predictions for our universe as we will discuss later. We review a number of conjectures which are aimed at distinguishing the swampland from the landscape.The string landscape and the swampland will be the topic of the first two lectures. In the third lecture, which is on a somewhat disjoint topic, we review critically where we are in our current understanding o...

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Section: Pos(tasi2017)015mentioning

confidence: 99%

“…In this way, the quiver gauge theory is derived from first principles by living on the intersecting D6-branes under the mirror symmetry map of the D3-branes probing the Calabi-Yau singularity. See [127,128,129] for more details.…”

Section: Pos(tasi2017)015mentioning

confidence: 99%

The String Landscape, the Swampland, and the Missing Corner

Vafa¹,

Brennan²,

Carta³

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

142

209

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“…The dimer can be JHEP05(2014)001 obtained from the toric diagram using various inverse algorithms (e.g. [43][44][45]). Numbered faces in the dimer correspond to gauge groups, common nodes of faces to bi-fundamental matter, and the "±" faces correspond to superpotential terms.…”

Section: Visible Sector D-branesmentioning

confidence: 99%

Explicit de Sitter flux vacua for global string models with chiral matter

Cicoli

Klevers

Krippendorf³

et al. 2014

J. High Energ. Phys.

137

222

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Abstract:We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider CalabiYau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α ′ corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP 6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP 3 singularity.

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“…• Brane Tilings (Dimers) [41][42][43][44][45][46][47] can be used to represent D3-brane worldvolume theories whose vacuum moduli space is toric Calabi-Yau. A brane tiling encodes the bifundamental matter content (quiver) and superpotential of the gauge theory.…”

Section: Reflexive Polytopesmentioning

confidence: 99%

Brane tilings and reflexive polygons

Hanany

Seong

2012

Fortschritte der Physik

106

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Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories of D3 branes with toric Calabi-Yau moduli spaces that are conveniently described with brane tilings. We find all 30 theories corresponding to the 16 reflexive polygons, some of the theories being toric (Seiberg) dual to each other. The mesonic generators of the moduli spaces are identified through the Hilbert series. It is shown that the lattice of generators is the dual reflexive polygon of the toric diagram. Thus, the duality forms pairs of quiver gauge theories with the lattice of generators being the toric diagram of the dual and vice versa.

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Brane tilings and their applications

Cited by 126 publications

References 348 publications

The String Landscape, the Swampland, and the Missing Corner

The String Landscape, the Swampland, and the Missing Corner

Explicit de Sitter flux vacua for global string models with chiral matter

Brane tilings and reflexive polygons

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