探索16到32超对称增强的无限重整化群流动

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本文档探讨了一项关于无限组重整化群流的研究，其焦点在于从具有16个超对称量子数（supercharges）的理论出发，通过一系列的流动过程，最终达到具有32个超对称（Poincaré plus special）的超共形场理论（Superconformal Field Theory，SCFT）。这一研究起始于紫外线（UV）固定点，即那些尚未发现拉格朗日描述的强大四维N = 2 SCFTs，它们表现出强烈的相互作用性。在量子场论的框架下，这样的理论通常难以用传统的局部化描述，因为它们可能涉及到非perturbative效应或者深层次的对称性结构。作者们，来自伦敦皇后玛丽大学物理与天文学学院以及日本立命馆大学理学部物理科学系，着手研究这些超对称增强的重整化群流，旨在揭示这些非平凡理论间的关联及其可能的物理意义。他们关注的是如何通过流动力学的方法，探索这些高超对称性的理论空间，并寻找潜在的新物理现象或理论一致性检验的机会。关键词包括“扩展超对称”和“规范场论”，这表明他们的工作不仅限于理论探讨，还可能涉及到实际的物理应用，如粒子物理学和弦理论中的超对称模型的扩展。文章引用了预印本ArXiv的版本号1807.02785，并强调了开放获取的特性，这表明研究成果可供全球科研人员无限制地访问和利用。值得注意的是，该论文是SCOAP3项目资助的产物，SCOAP3是一个旨在提供开放获取服务的科学合作组织，旨在促进物理学领域的知识共享。论文的发表日期为2018年10月，收录在《Journal of High Energy Physics》的10月刊中，编号为175，标志着这一领域的重要研究进展。这项工作对于理解超对称性在量子场论中的角色，特别是在非平凡的理论框架下，提供了宝贵的洞见，并为未来寻找新的理论框架和物理模型打开了新的研究方向。它强调了在理论物理学中的数学工具和技术在探索未知物理领域的关键作用。

JHEP10(2018)175

Combined with a gauge ﬁeld on C, the conﬁguration in (2.1) forms a solution to

Hitchin’s equations and describes the Higgs branch of the mirror of the S

reduction of

our 4D theories of interest (the reduction of the 5D theory on C). Therefore, it describes

the Coulomb branch of the direct S

reduction and also, via the base of the corresponding

ﬁbration, the Coulomb branch of the 4D theory itself. For example, the Seiberg-Witten

curve of the 4D theory may be read oﬀ from the spectral curve [23, 24]

det(x − Φ

) = 0 . (2.2)

In order for the description of the moduli space to not jump discontinuously as a

function of the parameters residing in the T

, a suﬃcient condition on the T

is that they

are regular

semisimple (see [26] and references therein for a discussion in a closely related

context). In particular, this statement means that the T

can be brought to the form

of diagonal matrices with non-degenerate eigenvalues. These singularities give rise to 4D

theories with Coulomb branch operators of non-integer scaling dimensions and generalize

the theories described in [27, 28].

The above class of theories, while very broad, is (modulo some caveats we will discuss)

not closed under the natural SCFT operation of conformal gauging [30] or under the RG

ﬂow. In fact, these SCFTs form a part of a much broader but still relatively poorly

understood class of theories called the “type III” theories [23] (these theories are expected

to exhibit various interesting phenomena; e.g., see [22, 31–33]).

To deﬁne the type III SCFTs, we relax the condition of regularity of the T

. In this

case, the requirement of smoothness away from the origin of the moduli space implies

that [26]

−1

⊆ L

⊆ · · · ⊆ L

`−2

, (2.3)

where the L

are the Levi subalgebras associated with the T

This restriction can be

conveniently described in terms of certain Young diagrams [23]

↔ Y

= [n

i,1

, n

i,2

, · · · , n

i,k

] , n

i,a

≥ n

i,a+1

∈ Z

a=1

i,a

= N , (2.4)

where the columns of height n

i,a

represent the eigenvalue degeneracies of the T

. The

condition (2.3) amounts to the statement that Young diagram i and Young diagram i − 1

are related by taking some number of columns (possibly zero) in diagram i and decomposing

each of them into columns in diagram i − 1.

In this picture, the T

−1

matrix has a special status: it contains mass parameters (or,

equivalently, vevs for the corresponding background vector multiplets) of the theory. By

N = 2 SUSY, such mass parameters correspond to elements of the Cartan subalgebra

Note that the puncture of C is still irregular!

Just as in the case of regular singularities, irregular singularities may be enriched by the presence of

certain co-dimension one symmetry defects. Such a construction can lead to 4D SCFTs if there is also a

regular singularity present [29].

Speciﬁcally, L

is deﬁned as the centralizer (in A

N−1

) of the T

with a ≤ i ≤ ` − 2. Note that the

conditions in (2.3) are necessary but not suﬃcient to have a sensible SCFT.

– 3 –

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