349 research outputs found

    Exact partition functions of Higgsed 5d TNT_N theories

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    We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the TNT_N theory. The theories may be realized by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realized in various Higgs branches of the T3T_3 theory. A particularly interesting example is the E8E_8 theory which can be obtained by Higgsing the T6T_6 theory. We explicitly compute the partition function of the E8E_8 theory and find the agreement with the field theory result as well as the enhancement of the global symmetry to E8E_8.Comment: 54 pages, 13 figures, v2. added an appendix and minor changes in the main text, version accepted on JHE

    Topological vertex for Higgsed 5d TNT_N theories

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    We analyse the computation of the partition function of 5d TNT_N theories in Higgs branches using the topological vertex. The theories are realised by a web of (p,q)(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 E6E_6, E7E_7 and E8E_8 theories. Moreover we show how in some specific cases similar results can be extended to the computation of the partition function of 5d TNT_N theories in the Higgs branch using the refined topological vertex. These cases require a modification of the refined topological vertex.Comment: 60 pages, 23 figures. v2, corrected typos, version accepted on JHE

    5d/6d DE instantons from trivalent gluing of web diagrams

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    We propose a new prescription for computing the Nekrasov partition functions of five-dimensional theories with eight supercharges realized by gauging non-perturbative flavor symmetries of three five-dimensional superconformal field theories. The topological vertex formalism gives a way to compute the partition functions of the matter theories with flavor instanton backgrounds, and the gauging is achieved by summing over Young diagrams. We apply the prescription to calculate the Nekrasov partition functions of various five-dimensional gauge theories such as SO(2N)\mathrm{SO}(2N) gauge theories with or without hypermultiplets in the vector representation and also pure E6,E7,E8E_6, E_7, E_8 gauge theories. Furthermore, the technique can be applied to computations of the Nekrasov partition functions of five-dimensional theories which arise from circle compactifications of six-dimensional minimal superconformal field theories characterized by the gauge groups SU(3),SO(8),E6,E7,E8\mathrm{SU}(3), \mathrm{SO}(8), E_6, E_7, E_8. We exemplify our method by comparing some of the obtained partition functions with known results and find perfect agreement. We also present a prescription of extending the gluing rule to the refined topological vertex.Comment: 66 pages, 28 figures; v2: typos corrected, references added and a Mathematica notebook for some checks adde

    Charting Class Sk{\cal S}_k Territory

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    We extend the investigation of the recently introduced class Sk{\cal S}_k of 4d N=1\mathcal{N}=1 SCFTs, by considering a large family of quiver gauge theories within it, which we denote Sk1\mathcal{S}^1_k. These theories admit a realization in terms of Zk\mathbb{Z}_k orbifolds of Type IIA configurations of D4-branes stretched among relatively rotated sets of NS-branes. This fact permits a systematic investigation of the full family, which exhibits new features such as non-trivial anomalous dimensions differing from free field values and novel ways of gluing theories. We relate these ingredients to properties of compactification of the 6d (1,0) superconformal TNk{\cal T}_N^k theories on spheres with different kinds of punctures. We describe the structure of dualities in this class of theories upon exchange of punctures, including transformations that correspond to Seiberg dualities, and exploit the computation of the superconformal index to check the invariance of the theories under them.Comment: 44 pages, 24 figure

    Mass-deformed TNT_N as a linear quiver

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    The TNT_N theory is a non-Lagrangian theory with SU(N) flavor symmetry. We argue that when mass terms are given so that two of SU(N)'s are both broken to SU(N-1) x U(1), it becomes TN1T_{N-1} theory coupled to an SU(N-1) vector multiplet together with N fundamentals. This implies that when two of SU(N)'s are both broken to U(1)N1^{N-1}, the theory becomes a linear quiver. We perform various checks of this statement, by using the 5d partition function, the structure of the coupling constants, the Higgs branch, and the Seiberg-Witten curve. We also study the case with more general punctures.Comment: 36 pages, 5 figures; v2: short discussions on 3d T_N theory appended, typos corrected, and references adde

    Topological strings and 5d T_N partition functions

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    We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T_3 theory as well as Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T_N theory. We compute the partition function of the E_7 theory via this prescription, and find the E_7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.Comment: 79 pages, 27 figures; v2: minor improvements, references adde