BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories

Alim, Murad; Cecotti, Sergio; Córdova, Clay; Espahbodi, Sam; Rastogi, Ashwin; Vafa, Cumrun

doi:10.1007/s00220-013-1789-8

Cited by 138 publications

(333 citation statements)

References 59 publications

(147 reference statements)

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“…These theories can be constructed for type g = A N−1 13 by compactifying N M5-branes on a Riemann surface Σ × R 4 with the same topological twist, where Σ → C is a multisheeted cover of C. This derives the data of the Seiberg-Witten curve and Seiberg-Witten 1-form, where the curve the Prym variety 14 associated to the map Σ → C [40,41,46]. In addition, this gives a clear geometric way to study the BPS spectrum, line operators, surface operators, and expectation values of supersymmetric operators in the associated four dimensional theory [47,48,49,50,51,52,53,54,55]. See [56,57,58,44] for a more general review.…”

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)

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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 addition, this gives a clear geometric way to study the BPS spectrum, line operators, surface operators, and expectation values of supersymmetric operators in the associated four dimensional theory [47,48,49,50,51,52,53,54,55]. See [56,57,58,44] for a more general review.…”

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)

Self Cite

142

209

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“…The simplest non-trivial N = 2 SCFT with a Lagrangian description is SQCD with gauge group SU(2) and four fundamental quarks. We choose its BPS quiver in the form [42][43][44] c 1…”

Section: Su(2) Sqcd With N F = 4 and S-dualitymentioning

confidence: 99%

“…BPS states in the same orbit of the Galois symmetry are automatically mutually-local. SU (2) with N f = 4 has a strongly-coupled finite BPS chamber with 12 hypermultiplets [42][43][44], which is invariant under the Z 2 symmetry ι in the sense that if γ ∈ Γ is the charge of a stable hypermultiplet so is ι(γ). Indeed the set of the charge vectors of the 12 hypermultiplets is given by the union ∆ + ∆ + of the positive roots ∆ + of the two A 3 Dynkin full subquivers over the nodes {a 1 , a 2 , c 1 } and {b 1 , b 2 , c 2 } which are interchanged by ι [42,44,45].…”

Section: Su(2) Sqcd With N F = 4 and S-dualitymentioning

confidence: 99%

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

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We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr M N where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A N . This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S 2 × T 2 where we turn on 1 2 N units of U(1) r flux on S 2 .

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“…for example [5,18,19]) and Physics (cf. for example [1,2,8,22]), with the compatibility between ideal flips and QP-mutations proved in [14] appearing as well.…”

Section: Introductionmentioning

confidence: 99%

Quivers with potentials associated to triangulated surfaces, part IV: removing boundary assumptions

Labardini-Fragoso

2015

Sel. Math. New Ser.

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We prove that the quivers with potentials associated with triangulations of surfaces with marked points, and possibly empty boundary, are non-degenerate, provided the underlying surface with marked points is not a closed sphere with exactly five punctures. This is done by explicitly defining the QPs that correspond to tagged triangulations and proving that whenever two tagged triangulations are related to a flip, their associated QPs are related to the corresponding QP-mutation. As a byproduct, for (arbitrarily punctured) surfaces with non-empty boundary, we obtain a proof of the non-degeneracy of the associated QPs which is independent from the one given by the author in the first paper of the series. The main tool used to prove the aforementioned compatibility between flips and QP-mutations is what we have called Popping Theorem, which, roughly speaking, says that an apparent lack of symmetry in the potentials arising from ideal triangulations with self-folded triangles can be fixed by a suitable right-equivalence.

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BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories

Cited by 138 publications

References 59 publications

The String Landscape, the Swampland, and the Missing Corner

The String Landscape, the Swampland, and the Missing Corner

Superconformal index, BPS monodromy and chiral algebras

Quivers with potentials associated to triangulated surfaces, part IV: removing boundary assumptions

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