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首页D3线相交有效场论的高阶分析与一致性
本文主要探讨了关于D3线相交的有效场论,这是一项在弦理论与量子场论中的重要研究课题。D3-brane 是M理论和超弦理论中的基本对象,它们是额外维度中的一种物体,对于理解多元宇宙和强相互作用有着关键作用。在这个特定的研究中,作者Reza Abbaspur关注的是两个D3-brane的特殊情况,这两个brane在一个最近提出的维度线上相交,这与[1]中的理论框架紧密相关。 在扰动理论的背景下,作者开发了一种系统的方法,用于从经典有效作用中推导出任意阶的理论。这种方法的关键在于处理在所有阶次的摄动序列中可能出现的对数散度问题。对数散度是量子场论中的一个常见挑战,它源自于无穷小的短距离行为,通常需要通过重整化过程进行处理。在这里,作者采用了一种适当的重整化处方,成功地得到了参考文献[1]中的一阶重整化群方程,这是理论的一个重要基石,它描述了参数随能量尺度变化的动态演化。 不仅如此,文章还揭示了一组无限数量的高阶方程,这些方程在理论的精确性上进一步增强了有效性。它们与一阶方程的兼容性被细致地验证,这表明这些高阶方程并非孤立存在,而是构成了一个完整的理论体系。这一发现对于深化对D3-brane相互作用的理解以及探索更深层次的物理现象具有重要意义。 总结来说,这篇论文不仅发展了D3-brane有效场论的计算技术,还提供了理论框架的一次重要拓展,对理解弦理论中的相交效应、非perturbative效应以及量子场论中的重整化方法都做出了贡献。通过这些高阶方程,研究者能够更好地预测和解释复杂的物理过程,尤其是在黑洞物理学和早期宇宙的模型构建中。
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Physics Letters B 780 (2018) 647–654
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
On the effective field theory of intersecting D3-branes
Reza Abbaspur
Department of Physics, School of Sciences, Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 February 2018
Accepted
28 March 2018
Available
online 3 April 2018
Editor:
N. Lambert
Dedicated
to the memory of Joseph
Polchinski the great physicist of all time
We study the effective field theory of two intersecting D3-branes with one common dimension along
the lines recently proposed in ref. [1]. We introduce a systematic way of deriving the classical effective
action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle
logarithmic divergencies arising at all orders in the perturbation series, we recover the first order
renormalization group equation of ref. [1]plus an infinite set of higher order equations. We show the
consistency of the higher order equations with the first order one and hence interpret the first order
result as an exact RG flow equation in the classical theory.
© 2018 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction and summary
There has been a longtime interest in realizing phenomenolog-
ically
attractive models of field theory in the framework of string
theory [2]. Since the advent of D-branes [3], various supersym-
metric
field theories have been constructed using brane setups
that preserve some amount of the spacetime supersymmetry [4].
Aprivilege of using these brane realizations is their role in provid-
ing
direct geometric interpretations for the physical phenomena in
the underlying field theories.
A
primary example of such brane setups is the 1/2 BPS system
of two coincident D3-branes having a low-energy limit descrip-
tion
in terms of a 4-dimensional non-abelian U(2) gauge theory
with N = 4 supersymmetry. The massless modes of open strings
ending on D3-branes in this limit are described by the U(2) ad-
joint
fields in this gauge theory. In the symmetry broken phase
(U (2) → U (1) ×U (1)) this theory gives the low-energy description
of a pair of parallel D3-branes at a small separation of the order of
α
[5]. The F-strings stretched between the two branes in that limit
get a finite mass and are described by the off-diagonal components
of the U(2) adjoint fields in the gauge theory. In the S-dual picture,
these F-strings become D-strings having a low-energy description
as solitons of the type of BPS magnetic monopoles in the gauge
theory [6].
A
more intriguing example in this context is the 1/4 BPS sys-
tem
of two orthogonally intersecting D3-branes sharing a common
spatial dimension and having a small separation of the order of α
E-mail address: abbaspur @modares .ac .ir.
in their overall transverse directions.
1
The field theory model of
this system was first constructed and studied from a holographic
perspective in ref. [8]. The model action in this case consists of
the sum of the actions for two copies of a D = 4, N = 4 U (1)
gauge theory along the worldvolumes of the two branes plus a
term describing a charged N = (4, 4) hypermultiplet along their
(1 + 1)-dimensional intersection. The hypermultiplet fields corre-
spond
to the low-lying modes of the F-strings stretched between
the two branes with either of the two possible orientations. They
carry opposite charges of the U (1) gauge fields on the two branes
corresponding to opposite charges at the two ends of the F-strings.
The overall system possesses a common D = 4, N = 2 supersym-
metry
which corresponds to the preservation of 8 supercharges by
the brane system. Again in the S-dual picture, the F-strings become
D-strings but because of the abelian nature of the gauge theory on
D3-branes it is not clear how to describe them as magnetically
charged solitons in field theory.
The
proper solitonic description for the above system was pre-
sented
recently in a nice paper by Mintun, Polchinski and Sun
[1]. The authors showed that the hypermultiplet fields source both
electric and magnetic currents along the intersection. The mag-
netic
current is associated with a varying dipole density P along
the intersection, but the net magnetic charge vanishes if the hy-
permultiplet
action has the canonical form. This is mainly because
to keep the energy finite in this model, P must vanish at both
ends (at x
1
→±∞) along the intersection. The U(1) holonomy
along each brane on the other hand requires a periodicity in P
of the form P ∼ P +8π which translates to a certain periodicity
1
For a general review of the BPS configurations of intersecting branes see ref. [7].
https://doi.org/10.1016/j.physletb.2018.03.082
0370-2693/
© 2018 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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