阿贝尔三维镜下N=2 Argyres-Douglas理论的拉格朗日描述与四维N=1对称性流动

136 浏览量更新于2024-07-16 收藏 747KB PDF 举报

本文主要探讨了N=2的Argyres-Douglas理论的拉格朗日描述，这是一种在弦理论和量子场论中具有重要意义的理论模型。Argyres-Douglas模型以其独特的红外行为和非平凡的对称性吸引着物理学家的注意。作者利用近期对顺序约束的新理解，尝试推测所有具有Abelian三维镜像的Argyres-Douglas模型的拉格朗日量。这些模型通常与四维N=1的颤动类相联系，例如(Ak,AkN+N-1)模型，它们在低能量尺度下展现出通用Argyres-Douglas理论的行为。文章深入研究了N=1的手性环如何映射到N=2的CFT（二维康威模）中的库仑分支和希格斯分支。这种映射关系揭示了理论之间的相互作用和对称性的转换。在三维镜像的背景下，通过重力动力学的重整化群流动(RG flow)，这些理论被映射到N=4的完整图颤动上，这是更高维度下理论结构的体现。此外，作者还对规范理论对偶(A1,D4)进行了压缩到三维的研究，发现了一个有趣的对偶性，即该理论可以被压缩成一个具有三种味道的N=4 SQED (超量子电动力学)。这一发现不仅提供了理论模型的简化形式，也揭示了不同理论间的相互关联。这篇论文是N=2 Argyres-Douglas理论领域的重要进展，它不仅深化了我们对这些特殊理论结构的理解，也为未来的理论探索和实验证据的寻找提供了新的线索。读者可以借此了解拉格朗日描述在理解这些复杂理论中的核心作用，以及它们与更高级别的理论框架之间的桥梁。

JHEP10(2017)106

in the bifundamental representation one abelian gauge factor is redundant and can be

dropped. We cho ose to decouple the vector multiplet U(1)

, so the cartan subgroup of

the SO ( 8) global symmetry of the theory is described by the topological symmetries of the

four remaini ng nodes. In the following we will only need to consider the SU(3) symmetry

associated with the nodes U(1)

and U(2). The singlets in the abel i an vector multiplets

will be denoted ϕ

(i = 1, 2, 3) whereas the trace and traceless parts of the U(2) adjoint are

and φ

respectively. The operators Trφ

and the monopole of SU(2) SQCD are mapped

on the mirror side to

and

respectively.

The SO(8) global symmetry of SQCD arises quantum mechanical l y in the mirror the-

ory: the Cartan subgroup U(1)

corresponds to the topological symmetry assoc i at ed with

the four abelian gauge gr oups in ﬁgure

2.7, whereas the other generators are related to

monopole operators of dimension one, whose multiplets contain conserved currents ([

18]).

In the rest of the paper we only need to consider the SU(3) subgroup associated with the

gauge groups U(1)

and U(2). The map between oﬀ-diagonal components of the meson

and monopoles is as follows:







˜q







↔







−0

−−

0−







(2.8)

The two Cartan components of the me son matrix are mapped to ϕ

and

. In (

2.8) we

have included only the charges under the topological symmetries related to U(1)

and U(2),

the others being trivial.

The mirror of T

′

3d,U V

and (A

, D

) AD theory

Using the results reviewed before, we ﬁnd that the mirror dual of T

′

3d,UV

is the gauge theory

in (2.7) with superpotential

W =

−

− Tr

+ M

+,0

+ M

0,+

+ α

−−

+β

(

+ 2

). (2.9)

where we included the dynamically generated monopole term.

We now use the monopole duality discovered in [

5] (see also [19, 20] for previous Abelian

examples and [

21] for a brane inte r pr e tat i on) , which in the case of interest to us states that

a 3d N = 2 theory U(N

− 1) with N

ﬂavors and W = M

is dual to a Wess-Zumino

model with superpotential

W = γ

det(X

) (2.10)

Before proc ee di ng, we would like to remark that in what follows the two numerical

coeﬃcients of the β

term in (

2.9) could be replaced by two arbitrary numbe r s without

aﬀecting the ﬁnal result. The important point is that the β

term in (

2.9) is not proportional

to β

, as we woul d get if in (

2.9) we neglected the mirror of the superpotential term

– 7 –

JHEP10(2017)106

1 12

Figure 1. Mirror of T

′

3d,UV

after conﬁnement of the U(1)

gauge gr oup.

According to the monopole duality, the gauge group U(1)

conﬁnes leaving behind the

U(2) adjoint chiral X

. The theory (2.9) now becomes as in ﬁgure 1 with supe r potential

W = ϕ

TrX

i>1

−

TrX

i>1

− Tr

i>1

+γ

det X

+ M

+ α

−

+ β

(

+ 2

). (2.11)

In this formula M

denote the monopoles charge d under the topol ogi c al symmetry asso-

ciated with the U(2) gauge node. As is clearly displayed by the superpotential, X

and

become massive and can be integrated out. At this stage the U(2) gauge group has

three ﬂavors and no adjoint matter, so according to the monopol e duality it conﬁnes and is

traded for a 3 × 3 chiral multiplet X

, which is nothing but the dual of

(i, j = 2, 3, 4).

This also generates the superpotential term γ

det X

. Notice that the equations of motion

of (

2.11) impose the constraint X

= −

i>1

. Using this fact we can express det X

terms of traces of X

det X

(TrX

)

− TrX

(

)

− Tr((

)

(TrX

)

− TrX

. (2.12)

Notice that in theory (1) the cartan subgroup of the U(3) symmetry under which

(i, j = 2, 3, 4) transforms in the adjoint representation is gauged: the U(1)

2,3,4

symmetries

are generated respectively by the 3 × 3 matrices diag(1, 0, 0), diag(0, 0, 1) and diag(0, 1, 0).

Our convention will be that these groups act in the same way on the matrix X

after

conﬁnement of the U(2) gauge group. As a result, the oﬀ-diagonal components of X

become bifundamental hypermultiplets charged under the leftover U(1)

symmetries and

we relabel the ﬁelds as follows:

)

, (X

)

↔ p

, ˜p

; (X

)

, (X

)

↔ p

, ˜p

; (X

)

, (X

)

↔ p

, ˜p

After conﬁnement of the U(2) gauge group the theory in ﬁgure

1 becomes as in ﬁgure 2

The ﬁelds ϕ

now only appear in the superpotential terms

W = (ϕ

−

)(X

)

+ (ϕ

−

)(X

)

. . . (2.13)

As a conseq u enc e they become massive and their F-terms set to zero the diagonal compo-

nents of X

. The remaining ﬁelds ar e α

, β

, γ

2,3

and p

, ˜p

with superpot ential

W = −

˜p

+ β

(˜p

+ 2˜p

) + γ

det X

+ α

. (2.14)

– 8 –

剩余40页未读，继续阅读

weixin_38720322

粉丝: 4
资源: 921

阿贝尔三维镜下N=2 Argyres-Douglas理论的拉格朗日描述与四维N=1对称性流动

N $$ \ mathcal {N} $$ = 1拉格朗日方程用于广义Argyres-Douglas理论

拉格朗日插值多项式：拉格朗日插值多项式-matlab开发

拉格朗日多项式插值：拉格朗日多项式插值-matlab开发

拉格朗日lagrange-multipliers.pdf

拉格朗日插值法-Python实现示例

拉格朗日乘子法-fmincon,拉格朗日乘子法原理,matlab

拉格朗日方程：拉格朗日是计算运动方程的函数（拉格朗日方程）-matlab开发

3.1.0 拉格朗日算法基础-张满满1

拉格朗日乘子法-fmincon,拉格朗日乘子法原理,matlab源码.zip

拉格朗日乘子法-fmincon_乘子法_拉格朗日乘子法_拉格朗日求解_朗格朗日乘子_拉格朗日乘子

最新资源