Explicit analysis of Kähler deformations in 4D N=1 supersymmetric quiver theories

Haddou, Malika Ait Ben; Saidi, El Hassan

doi:10.1016/j.physletb.2003.09.029

Cited by 13 publications

(16 citation statements)

References 7 publications

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“…(ii) the generating functional of 3d partitions are captured by the local vertex operators 14) and its dual Ψ + (1). These Ψ ± operators will be denoted later as 15) but to keep the notations simpler, we will momentary use Ψ ± (z) and come later to the Γ…”

Section: Plane Partitions and 3d-hilbert Statesmentioning

confidence: 99%

“…Recently, these functions have known a revival of interest in connection with topological string theory [8,9,10]; in particular in the study of BPS black holes, given by branes wrapping collapsed cycles in CalabiYau orbifolds, and in the infinite n limit of quiver gauge theories [11,12,13,14,15]. MacMahon functions G 2 (q) and G 3 (q) are also used in the explicit computation of the amplitudes of A-model topological string on local Calabi-Yau manifolds [16,17,5,18].…”

Section: Introductionmentioning

confidence: 99%

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Generalized MacMahon Gd(q) as q-deformed CFT2 correlation function

Drissi¹,

Jehjouh²,

Saidi

2008

Nuclear Physics B

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Using Γ ± (z) vertex operators of the c = 1 two dimensional conformal field theory, we give a 2d-quantum field theoretical derivation of the conjectured ddimensional MacMahon function G d (q). We interpret this function G d (q) as a (d + 1)-point correlation function G d+1 (z 0 , ..., z d ) of some local vertex operators O j (z j ). We determine these operators and show that they are particular composites of q-deformed hierarchical vertex operators Γ

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Section: Plane Partitions and 3d-hilbert Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized MacMahon Gd(q) as q-deformed CFT2 correlation function

Drissi¹,

Jehjouh²,

Saidi

2008

Nuclear Physics B

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“…The rule is as follows [5]: To the i-th node of D q , one associates a gauge multiplet V i and a chiral matter one Φ i transforming in adjoint representation of…”

Section: Supersymmetric Actionmentioning

confidence: 99%

RG cascades in hyperbolic quiver gauge theories

Laamara¹,

Haddou²,

Belhaj

et al. 2004

Nuclear Physics B

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In this paper, we provide a general classification of supersymmeric QFT4s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super QFT4s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT4s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made.

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“…This occurs in many areas of statistical physics [1][2][3] and topological string theory [4][5][6], BPS black holes, models of branes wrapping collapsed cycles in Calabi-Yau orbifolds, and quiver gauge theories [7][8][9]. Generalized MacMahon functions are used, in particular, in the computation of amplitudes of the A-model topological string [10][11][12][13], more specifically as regards the so-called topological vertex.…”

Section: Introductionmentioning

confidence: 99%

Generalized $$q$$ q -deformed correlation functions as spectral functions of hyperbolic geometry

2014

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We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with p ≤ 3, is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to p > 3. With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of threedimensional hyperbolic geometry.

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Explicit analysis of Kähler deformations in 4D N=1 supersymmetric quiver theories

Cited by 13 publications

References 7 publications

Generalized MacMahon Gd(q) as q-deformed CFT2 correlation function

Generalized MacMahon Gd(q) as q-deformed CFT2 correlation function

RG cascades in hyperbolic quiver gauge theories

Generalized $$q$$ q -deformed correlation functions as spectral functions of hyperbolic geometry

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