全息超对称彩色超导体：有限等位旋密度下的对称性破坏

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本文主要探讨了一种在高维度物理理论中，通过全息术（holography）研究的特殊现象——全息超对称彩色超导体。这种理论基于d=4（四维）的N=4超杨米尔斯理论，该理论与少量夸克味道（N_f≪N_c）相互作用。作者们引入了等位旋化学势μ_I，通过改变夸克的质量M_q，使得理论处于有限的等位旋密度n_I下。同时，他们还开启了两个R对称电荷密度n_1 = n_2。核心发现是，理论的基态呈现出超对称性，即部分超对称性和局部对称性以及部分规范对称性的自发破缺，形成了一种特殊的超流体状态，即超对称彩色超导体。这种状态允许在有限密度下保持部分对称性，而不会完全破坏对称性。全息描述中，这个现象通过AdS5×S5空间中的N_f个D7探针来实现，其对称性破缺是由于与等位旋电荷关联的电场导致D7内部部分D3的溶解。理论的无质量质谱包含了戈德斯通玻色子和铁离子超伴侣，这些是超对称性破缺后的基本粒子。如果等位旋密度n_I远小于μ_I的立方，那么大尺度的光谱将包含长寿命的介子准粒子；反之，若n_I接近μ_I的立方，准粒子可能不稳定。尽管存在质量和电荷密度，但文章强调了共形不变性和相对论不变性在红外区域仍然作为对称性出现的可能性。这表明，尽管系统在特定条件下经历了对称性破缺，但在宏观尺度上，这些基本的对称性原理依然在起作用。这篇论文利用全息技术深入研究了高能量物理学中的一种新奇状态，揭示了超对称性和超导性在特定条件下的结合，并对量子场论中的对称性破缺和量子态的性质提供了新的见解。这一成果不仅对于理解高能物理的微观世界具有重要意义，也为理论物理学家提供了新的实验预测和可能的研究方向。

JHEP05(2019)106

We will investigate a simple yet extremely rich holographic model which exhibits both

color superconductivity and superﬂuidity when a certain combination of conserved charges

is taken to be large. Our model diﬀers from QCD in many respects, including the fact that

it is supersymmetric, that it exhibits no chiral symmetry and hence no pions, and that it

possesses an R-symmetry that is absent in QCD. Therefore we do not claim that our results

have any direct implications for real-world QCD. However, we believe that they are interest-

ing for three reasons. First, they show that color superconductivity does appear in hologra-

phy when some conserved charges are large (in this case a combination of isospin charge and

R-charge). Second, we expect that a similar holographic mechanism will give rise to color

superconductivity in the presence of baryon density [10]. Third, to the best of our knowl-

edge our model is the ﬁrst example of a supersymmetric color superconductor. Color su-

perconductivity in supersymmetric theories has been previously considered in e.g. [11–13],

but in these cases all the supersymmetries are broken by the ground state. In contrast,

in our model the ground state leaves some supersymmetry unbroken. We expect that this

property will facilitate a precise comparison between the strong-coupling limit described by

holography and the weak-coupling regime accessible via perturbative ﬁeld theory methods.

Color superconductivity in the holographic context has been previously explored.

Refs. [14, 15] considered baryon density instead of isospin density, ref. [16] studied a bottom-

up model instead of a top-down model, and refs. [17, 18] mimicked the breaking of the color

symmetry as the breaking of a global symmetry.

2 Model

Type IIB string theory on the near-horizon geometry of N

D3-branes and N

D7-branes is

dual to d = 4, N = 4, SU(N

) super Yang-Mills theory coupled to N

hypermultiplets in the

fundamental representation. The presence of the hypermultiplets breaks supersymmetry

to N = 2, so we will refer to this theory simply as “the N = 2 gauge theory”. Although

the hypermultiplets contain both bosons and fermions, we will loosely refer to them as

“ﬂavors” or “quarks”. In the regime N

 N

the D7-branes can be treated as probes [19]

in the AdS

× S

geometry

= H

−



−dt

+ d~x



+ H



+ dz



, (2.1)

where t, ~x are the four gauge theory directions parallel to the D3-branes, y

with i = 1, . . . , 4

are the coordinates along the D7-branes orthogonal to the D3-branes, and z

with α = 1, 2

are the coordinates orthogonal to both sets of branes. We will often write the metric in

the y

directions in spherical coordinates as

= dr

+ r



+ ω



, (2.2)

where ω

are the left-invariant forms on S

. H is the usual harmonic function in the

six-dimensional space transverse to the D3-branes:

H =



+ z



, (2.3)

with L the radius of AdS

and S

– 2 –

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