A
bstract
In this paper, we study 5d
N
= 1 Sp(
N
) gauge theory with
N
f
(
≤
2
N
+ 3) flavors based on 5-brane web diagram with
O
5-plane. On the one hand, we discuss Seiberg-Witten curve based on ...the dual graph of the 5-brane web with
O
5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with
O
5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with
O
5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.
A
bstract
Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three ...parameter family of SQCD theories, given by the number of colors
N
c
for an SU
N
c
gauge theory, number of fundamental flavors
N
f
, and the Chern Simons level
k
. The study of their infinite coupling Higgs branch is a long standing problem and reveals a rich pattern of moduli spaces, depending on the 3 values in a critical way. For a generic choice of the parameters we find a surprising number of 3 different components, with intersections that are closures of height 2 nilpotent orbits of the flavor symmetry. This is in contrast to previous studies where except for one case (
N
c
= 2
, N
f
= 2), the parameters were restricted to the cases of Higgs branches that have only one component. The new feature is achieved thanks to a concept in tropical geometry which is called
stable intersection
and allows for a computation of the Higgs branch to almost all the cases which were previously unknown for this three parameter family apart form certain small number of exceptional theories with low rank gauge group. A crucial feature in the construction of the Higgs branch is the notion of
dressed monopole operators
.
A
bstract
We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in
1
. We propose all the 5-brane web diagrams for these rank 2 ...theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for
G
2
gauge theory with six flavors and its dual Sp(2) and SU(3) gauge theories. We also present 5-brane webs for SU(3) theories of Chern-Simons level greater than 5.
A
bstract
For any 5d
N
= 1 superconformal field theory, we propose a “complete” prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, ...manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider SU(2) gauge theories with up to 7 flavors, Sp(2) gauge theories with up to 9 flavors, and Sp(2) gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.
A
bstract
We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from ...brane webs pioneered in
1
, by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ
2
gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.
6d SCFTs, 5d dualities and Tao web diagrams Hayashi, Hirotaka; Kim, Sung-Soo; Lee, Kimyeong ...
The journal of high energy physics,
05/2019, Volume:
2019, Issue:
5
Journal Article
Peer reviewed
Open access
A
bstract
We propose 5d descriptions of 6d
N
=
1
,
0
superconformal field theories arising from Type IIA brane configurations with an O8
−
-plane. We T-dualize the brane diagram along a ...compactification circle and obtain a 5-brane web diagram with two O7
−
- planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two O7
−
-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the SL(2, ℤ) duality of Type IIB string theory, leading to completely different group structure. These lead to a very rich class of dualities between 5d gauge theories whose UV completion is the same 6d superconformal field theory. We also explore Higgsing of the 6d theories and their 5d counterparts. Decoupling the same flavors from the dual 5d theories gives rise to another dual 5d theories whose UV completion is the same 5d superconformal field theory. Finally we propose the 6d description of 5d theories which is obtained by a generalization of 5d
T
N
theories with additional flavors, which turns out not to be in the class of Type IIA brane construction generically.
A
bstract
We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition ...functions of the 5d SU(3)
0
gauge theory with 10 flavors, which is UV-dual to the 5d Sp(2) gauge theory with 10 flavors, based on two different 5-brane web diagrams, and check that two partition functions agree with each other. Then, by utilizing the geometric transition, we find the surface defect partition function for E-string on ℝ
4
×
T
2
. We also discuss that our result is consistent with the elliptic genus. Based on the result, we show how the global symmetry is broken by the defects, and discuss that the breaking pattern depends on where/how we insert the defects.
Rank-3 antisymmetric matter on 5-brane webs Hayashi, Hirotaka; Kim, Sung-Soo; Lee, Kimyeong ...
The journal of high energy physics,
05/2019, Volume:
2019, Issue:
5
Journal Article
Peer reviewed
Open access
A
bstract
We discuss Type IIB 5-brane configurations for 5d
N
=
1
gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow ...from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
A
bstract
We propose a new 5d description of the circle-compactified 6d (
D
N
+ 4
, D
N
+ 4
) minimal conformal matter theory which can be approached by the 6d
N
=
1
0
Sp(
N
) gauge theory with
N
f
= ...2
N
+ 8 flavors and one tensor multiplet. Compactifying the brane set-up for the 6d theory, we arrive at a 5-brane Tao diagram for 5d
N
=
1
SU(
N
+ 2) theory of the vanishing Chern-Simons level with 2
N
+ 8 flavors. We conjecture that the 6d theory is recovered as the UV fixed point of this 5d theory. We show that the global symmetry of this 5d theory is SO(4
N
+ 16) identical to that of the 6d theory by analyzing the 7-brane monodromy. By using the Tao diagram, we also find the instanton fugacity is exactly given by the circle radius. By decoupling flavors in this 5d theory, one can obtain all the 5d SU(
N
+ 2) gauge theories of various Chern-Simons levels and corresponding enhanced global symmetries at the 5d UV fixed point.
A
bstract
In this article we use 5-brane junctions to study the 5D
T
N
SCFTs corresponding to the 5D
= 1 uplift of the 4D
= 2 strongly coupled gauge theories, which are obtained by compactifying
N
...M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D super-conformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and
n
-point functions of the
q
-deformed
W
N
Toda theories.
PDF
