From strings in 6d to strings in 5d

Self Cite

M5 branes probing D-type singularities give rise to 6d (1,0) SCFTs with SO × SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits.

Section: Discussionmentioning

confidence: 99%

D-type fiber-base duality

Haghighat

Kim

Yan

et al. 2018

Self Cite

“…Let us also notice that E-strings BPS state counting in terms of elliptic genera can be realized as twisted N = 4 partition functions [53][54][55]. These partition functions enjoy interesting and non-trivial modular properties [56].…”

Section: Discussionmentioning

confidence: 99%

Exact results for N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

Bershtein

Bonelli

Ronzani

et al. 2016

We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N ) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2 * theory on P 2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

“…Finally, there has recently been a lot of progress in computing the elliptic genera of strings in six-dimensional superconformal field theories [46][47][48][49][50][51][52][53] and also the elliptic genera of strings in five-dimensional superconformal field theories [54,55]. It would be interesting to see if our prescription can be applied to such computation.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Topological vertex for Higgsed 5d T N theories

Hayashi

Zoccarato

2015

Abstract:We analyse the computation of the partition function of 5d T N theories in Higgs branches using the topological vertex. The theories are realised by a web of (p, q) 5-branes whose dual description may be given by an M-theory compactification on a certain local non-toric Calabi-Yau threefold. We explicitly show how it is possible to directly apply the topological vertex to the non-toric geometry. Using this novel technique, which considerably simplifies the computation by the existing method, we are able to compute the partition function of the higher rank E 6 , E 7 and E 8 theories. Moreover we show how in some specific cases similar results can be extended to the computation of the partition function of 5d T N theories in the Higgs branch using the refined topological vertex. These cases require a modification of the refined topological vertex.