Duality between string junctions and D-branes on del Pezzo surfaces

Mohri, Kenji; Ohtake, Yukiko; Yang, Sung–Kil

doi:10.1016/s0550-3213(00)00655-6

Cited by 19 publications

(35 citation statements)

References 52 publications

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“…The relation between rank-one SW geometries and rational elliptic surfaces has appeared repeatedly in the string-theory literature -see in particular [24,[49][50][51][52][53][54][55][56][57]. More recently, Caorsi and Cecotti used the RES formalism to explore the physics of strictly four-dimensional N = 2 field theories [58], in relation to the Argyres-Lotito-Lü-Martone classification of rank-one 4d N = 2 SCFT [59][60][61][62].…”

Section: The U-plane Cb Configurations and Rational Elliptic Surfacesmentioning

confidence: 99%

“…The BPS states from the 2-chains Γ ⊂ S here correspond to string junctions on the W -plane, which are open-string networks connecting the D3-brane to the 7-branes in a supersymmetric fashion. Such string junctions have been extensively studied in the literature, in this very same context [53,56,[161][162][163][164][165]. Secondly, it is well-known in F-theory that sections of the elliptic fibration are related to abelian symmetries and to the global form of the 'gauge group' -see e.g.…”

Section: Local Mirror Rational Elliptic Surface and The F-theory Picturementioning

confidence: 99%

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The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Closset

Magureanu

2022

SciPost Phys.

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The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with E_nEn flavour symmetry. We study their UU-plane, which is the one-dimensional Coulomb branch of the theory on \mathbb{R}^4 \times S^1ℝ4×S1. The total space of the Seiberg-Witten (SW) geometry – the E_nEn SW curve fibered over the UU-plane – is described as a rational elliptic surface with a singular fiber of type I_{9-n}I9−n at infinity. A classification of all possible Coulomb branch configurations, for the E_nEn theories and their 4d descendants, is given by Persson’s classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the UU-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the UU-plane, matching the infrared expectation for the couplings A(U)A(U) and B(U)B(U) to the UV computation using the Nekrasov partition function.

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Section: The U-plane Cb Configurations and Rational Elliptic Surfacesmentioning

confidence: 99%

Section: Local Mirror Rational Elliptic Surface and The F-theory Picturementioning

confidence: 99%

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Closset

Magureanu

2022

SciPost Phys.

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“…We will denote such a Calabi-Yau threefold by X N and the corresponding mirror Calabi-Yau threefold by Y N . The mirror manifold Y N is given by the following equations [10,11,15,16,17]…”

Section: The Basis Of Hmentioning

confidence: 99%

“…Above z = 0 we have a smooth elliptic fiber and the 3-cycle S i wraps a 1-cycle C i of the this elliptic fiber which degenerates at z = z i . If C i and C j have the charge (p i , q i ) and (p j , q j ) then the intersection number, # (S i · S j ), is given by 3 [11]. A bilinear product which counts the number of fermionic zero modes of the string stretched between two sheaves f !…”

Section: Z−planementioning

confidence: 99%

Quiver Theories from D6-branes via Mirror Symmetry

Hanany¹,

Iqbal²

2002

J. High Energy Phys.

181

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We study N = 1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the mirror manifold. The type IIB (p, q) 5-brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver diagrams and the charges of the fractional branes. 5)∆ can be thought of as an imaginary root extending the E N algebra to an affine E N algebra [19]. We will see in the next section that ∆ can be used to construct a 3-cycle which is the mirror of 0-cycle on X N .Actually the same structure of affine E N algebra is present in H * (B N ). To see this consider two vector bundles V 1,2 on B N such that ch(V a ) = (r a , Σ a , ch(V a )) 2 . An

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“…The quiver matrix is just the intersection matrix of the 3-cycles. In terms of the fractional branes {F 1 , · · · , F K } (which are mirror to S a ) on X, on Type IIB side, this is given by [7,20,8,13] Q ab = X ch(F a ⊗ F * b )Td(X) .…”

Section: Introductionmentioning

confidence: 99%

Quiver theories, soliton spectra and Picard-Lefschetz transformations

Feng¹,

Hanany²,

He³

et al. 2003

J. High Energy Phys.

142

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Quiver theories arising on D3-branes at orbifold and del Pezzo singularities are studied using mirror symmetry. We show that the quivers for the orbifold theories are given by the soliton spectrum of massive 2d N =2 theory with weighted projective spaces as target. For the theories obtained from the del Pezzo singularities we show that the geometry of the mirror manifold gives quiver theories related to each other by Picard-Lefschetz transformations, a subset of which are simple Seiberg duals. We also address how one indeed derives Seiberg duality on the matter content from such geometrical transitions and how one could go beyond and obtain certain "fractional Seiberg duals." Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine equations which classify all quivers related by Picard-Lefschetz. Some of these Diophantine equations can also be obtained from the classification results of Cecotti-Vafa for the 2d N = 2 theories.where {S 1 , · · · , S K }, which form a basis of H 3 (Y, Z), are three cycles topologically equivalent to S 3 and n a is the wrapping number of cycle S a . The D6-brane wrapped on T 3 gives rise to a N = 1 D = 4 theory with gauge group G and quiver matrix Q given by [8,13] G = K a=1 U (n a ) , Q ab = S a · S b .(1.2)1 Also for non-toric singularities once the mirror manifold is determined.

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Duality between string junctions and D-branes on del Pezzo surfaces

Cited by 19 publications

References 52 publications

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Quiver Theories from D6-branes via Mirror Symmetry

Quiver theories, soliton spectra and Picard-Lefschetz transformations

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