Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups

Benini, Francesco; Eager, Richard; Hori, Kentaro; Tachikawa, Yuji

doi:10.1007/s11005-013-0673-y

Cited by 250 publications

(562 citation statements)

References 36 publications

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“…An investigation of the Witten index in a general class of (0,2) models was carried out in [24]. In our case the Witten index vanishes for all connected sigma models but permutation symmetries of the models allow us to introduce a nonvanishing modified index.…”

Section: Witten's Index and Its Generalizationmentioning

confidence: 99%

Making supersymmetric connectedN=(0,2)sigma models

Shifman¹,

Vainshtein²,

Yung³

2015

Phys. Rev. D

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We construct "connected" (0,2) sigma models starting from n copies of (2,2) CP(N − 1) models. General aspects of models of this type (known as T + O deformations) had been previously studied in the context of heterotic string theories. Our construction presents a natural generalization of the non-minimally deformed (2,2) model with an extra (0,2) fermion superfield on tangent bundle T CP(N −1)×C 1 . We had thoroughly analyzed the latter model previously, found the exact β function and a spontaneous breaking of supersymmetry. In contrast, in certain connected sigma models the spontaneous breaking of supersymmetry disappears. We study the connected sigma models in the large-N limit finding supersymmetric vacua and determining the particle spectrum. While the Witten index vanishes in all the models under consideration, in these special cases of connected models one can use a permutation symmetry to define a modification of the Witten index which does not vanish. This eliminates the spontaneous breaking of supersymmetry. We then examine the exact β functions of our connected (0,2) sigma models.

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Section: Witten's Index and Its Generalizationmentioning

confidence: 99%

Making supersymmetric connectedN=(0,2)sigma models

Shifman¹,

Vainshtein²,

Yung³

2015

Phys. Rev. D

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“…The gauge theory elliptic genus can be computed by performing a suitable contour integral of [18][19][20], with the integral measure given by the contributions from the fields listed in table 1. The integral representation for Z k is given by [21] …”

Section: The Elliptic Genus Of Iib Little Stringsmentioning

confidence: 99%

“…In fact, with generic FI term ξ (i) I , the Coulomb branch will be all lifted as U(1) N → U(1). Since the elliptic genus formula of [19,20] is computing the index of CFT with generic nonzero FI parameters, this formula will compute the unwanted Higgs branch index, with lifted Coulomb branch. Apart from the absence of the SU(2) L2 in UV, this is another reason that the above (4, 4) CFT is inconvenient for studying the little string physics.…”

Section: Jhep02(2016)170mentioning

confidence: 99%

Little strings and T-duality

Kim

Lee

2016

J. High Energ. Phys.

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We study the 2d N = 4 gauge theory descriptions of little strings on type II NS5-branes. The IIB strings on N NS5-branes are described by the N = (4, 4) gauge theories, whose Higgs branch CFTs on U(N ) instanton moduli spaces are relevant. The IIA strings are described by N = (4, 4)Â N −1 quiver theories, whose Coulomb branch CFTs are relevant. We study new N = (0, 4) quiver gauge theories for the IIA strings, which make it easier to study some infrared observables. In particular, we show that the supersymmetric partition functions of the IIA/IIB strings on Omega-deformed R 4 × T 2 precisely map to each other by T-duality.

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“…, Φ d+2 ) = 0, where the Φ i denote the homogeneous coordinates of the weighted projective space and p is a transverse polynomial of degree m = i w i . We will now quickly review the results of [42] on how to calculate the elliptic genus for such manifolds.…”

Section: Calculating the Twined Elliptic Genusmentioning

confidence: 99%

“…The above can be further simplified by using properties of the θ-function (see appendix B of [42] for details). This leads to the following simple formula for the elliptic genus of a Calabi-Yau d-manifold that is a hypersurface in a weighted projective space and that can be described by a transverse polynomial: If we want to twine the elliptic genus by an Abelian symmetry that is generated by an element g acting via …”

Section: Jhep02(2018)129mentioning

confidence: 99%

Calabi-Yau manifolds and sporadic groups

Banlaki

Chowdhury

Kidambi

et al. 2018

J. High Energ. Phys.

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A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M 24 was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau d-folds for d > 3 have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.

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Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups

Cited by 250 publications

References 36 publications

Making supersymmetric connectedN=(0,2)sigma models

Making supersymmetric connectedN=(0,2)sigma models

Little strings and T-duality

Calabi-Yau manifolds and sporadic groups

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