JHEP01(2019)159
Eq. (2.6) and (2.7) lead to the following twisted chiral ring equation
(1 + q)P
N
(σ) = q
1
B
L
(σ) +
q
q
1
B
R
(σ) . (2.11)
Note that the two-dimensional scale µ drops from the equation, due to the same number
of chiral and antichiral. The twisted chiral ring relation (2.11) holds for all values of m
f
and so it can be set to zero.
The e
i
’s can be found from the Seiberg-Witten curve of the bulk theory [42, 43], which
can be written in the form
y
2
= (1 + q)
2
P
2
N
(x) − 4qB
N
f
(x) , (2.12)
with the SW differential,
λ = xd log ((1 + q)P
N
(x) + y) . (2.13)
Once e
i
is obtained, one can solve the chiral ring equation for σ order by order in q
1
and q.
Since the twisted superpotential W
∗
(σ
∗
(q
1
, q), q
1
) evaluated on a solution σ
∗
(q
1
, q)
satisfies
∂W
∂σ
σ
∗
= 0 , (2.14)
one obtains the following relation [29].
q
1
dW
∗
dq
1
= q
1
∂W
∗
∂q
1
= σ
∗
(2.15)
This can be compared with the corresponding equation computed from ramified instanton
partition function.
U(1) sigma model coupled to SU(2) SCFT. A simple surface operator in SU(2)
SCFT with N
f
= 4 hypermultiplets corresponds to the two-dimensional U(1) gauge theory
with four matter fields of charge 1,1,-1,-1 coupled to the four-dimensional theory. The
SU(2) SCFT is coupled to the vacuum manifold of the 2d theory, which is the total space
of O(−1)⊕O(−1) over CP
1
. The chiral ring equation (2.11) for the surface defect is written
(1 + q)
2
Y
i=1
(σ − e
i
) = q
1
2
Y
f=1
(σ − m
f
) +
q
q
1
2
Y
f=1
(σ + ˜m
f
) . (2.16)
In appendix A.1, e
i
’s are computed in terms of a and q. With a choice of classical vacuum,
a, we write σ as
σ = a +
X
i,j=1
s
ij
q
i
1
q
j
, (2.17)
and solve for s
ij
. Then one finds
σ
∗
= a +
q
1
2a
2
Y
i=1
(a − m
i
) +
q
2aq
1
2
Y
i=1
(a + ˜m
i
)
+
q
2
1
8a
3
(3a
2
+ a(m
1
+ m
2
) − m
1
m
2
)
2
Y
i=1
(a − m
i
)
+
q
2
8a
3
q
2
1
(3a
2
− a( ˜m
1
+ ˜m
2
) − ˜m
1
˜m
2
)
2
Y
i=1
(a + ˜m
i
) + · · · , (2.18)
where
P
m
f
=
P
˜m
f
= 0 can be imposed.
– 5 –
剩余26页未读，继续阅读
weixin_38609247
- 粉丝: 8
- 资源: 970
我的内容管理
展开
最新资源
- JDK 17 Linux版本压缩包解压与安装指南
- C++/Qt飞行模拟器教员控制台系统源码发布
- TensorFlow深度学习实践：CNN在MNIST数据集上的应用
- 鸿蒙驱动HCIA资料整理-培训教材与开发者指南
- 凯撒Java版SaaS OA协同办公软件v2.0特性解析
- AutoCAD二次开发中文指南下载 - C#编程深入解析
- C语言冒泡排序算法实现详解
- Pointofix截屏：轻松实现高效截图体验
- Matlab实现SVM数据分类与预测教程
- 基于JSP+SQL的网站流量统计管理系统设计与实现
- C语言实现删除字符中重复项的方法与技巧
- e-sqlcipher.dll动态链接库的作用与应用
- 浙江工业大学自考网站开发与继续教育官网模板设计
- STM32 103C8T6 OLED 显示程序实现指南
- 高效压缩技术：删除重复字符压缩包
- JSP+SQL智能交通管理系统：违章处理与交通效率提升
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
