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

By F. Benini, Richard Eager, K. Hori, Yuji Tachikawa. 2013

232 citations recorded by the source corpus.

We compute the elliptic genera of two-dimensional $${\mathcal{N} = (2, 2)}$$N=(2,2) and $${\mathcal{N} = (0, 2)}$$N=(0,2) -gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi–Yau, $${\mathcal{N} = (2, 2)}$$N=(2,2) SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric $${\mathcal{N} = (0, 2)}$$N=(0,2) model.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f7f6fcb9ae693115db6253f8605810c224c92801

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Citations in the corpus

Defects and quantum Seiberg-Witten geometry (2014, unknown): “See [57, 60, 99] for details.”
General instanton counting and 5d SCFT (2014, methodology): “There are various dangerous regions in the zero mode space, some analogous to those of the 2d index [25, 26] and some being intrinsic to the quantum mechanics.”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “ semiclassical monopole operators. The integrand Z m(x;y) contains classical and one-loop contributions. The derivation of (1.2) closely follows previous localization computations in related contexts [13, 14, 15, 6, 7, 8, 12, 16]. By summing over the uxes m in (1.2), one recovers the result of [9]: ”
Supersymmetric partition functions on Riemann surfaces (2016, methodology): “One of the assumptions in the derivation of the JK residue in [3, 6, 7] is that at each point u∗ ∈ Msing, the singular hyperplane arrangement is”
The geometry of supersymmetric partition functions (2013, background): “From the point of view of the (2, 0) theory on T (2), this partition function computes the elliptic genus, which is known to have modular properties under SL(2,Z) transformations of τ (see the recent papers [69-71] and references therein).”
Black hole microstates in AdS4 from supersymmetric localization (2015, background): “On a different note, let us also emphasize that the integral expression for the topologically twisted index found in [18], as the one for the elliptic genus in [59, 60], provides a novel type of large N “matrix models”: the integrands are standard, but they are integrated along non-trivial contours.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, methodology): “ection, we present explicit integral formulas for the M g;p S1 partition function. They can be derived by supersymmetric localization, similarly to the three-dimensional case studied in [27]|see also [22, 23, 17, 19, 20, 27]. We will only sketch this derivation, insisting on the specicities of the f”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “The resolution is the same as in [4].”