349 research outputs found

### Exact partition functions of Higgsed 5d $T_N$ theories

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 $T_N$ 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 $T_3$ theory. A particularly interesting example
is the $E_8$ theory which can be obtained by Higgsing the $T_6$ theory. We
explicitly compute the partition function of the $E_8$ theory and find the
agreement with the field theory result as well as the enhancement of the global
symmetry to $E_8$.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 $T_N$ theories

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.Comment: 60 pages, 23 figures. v2, corrected typos, version accepted on JHE

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

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 $\mathrm{SO}(2N)$ gauge theories with
or without hypermultiplets in the vector representation and also pure $E_6,
E_7, E_8$ 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
$\mathrm{SU}(3), \mathrm{SO}(8), E_6, E_7, E_8$. 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 ${\cal S}_k$ Territory

We extend the investigation of the recently introduced class ${\cal S}_k$ of
4d $\mathcal{N}=1$ SCFTs, by considering a large family of quiver gauge
theories within it, which we denote $\mathcal{S}^1_k$. These theories admit a
realization in terms of $\mathbb{Z}_k$ 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 ${\cal T}_N^k$
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 $T_N$ as a linear quiver

The $T_N$ 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 $T_{N-1}$ 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)$^{N-1}$, 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

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

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