论文标题
全息限制理论的散射长度
Scattering length in holographic confining theories
论文作者
论文摘要
构建了诸如QCD之类的狭窄理论的低能量有效理论描述，包括在衍生物扩张中组织的HADRON之间的局部相互作用。一旦确定了相关的低能自由度，这种方法也更普遍地适用于具有质量差距的理论。有效理论中局部相互作用的强度取决于散射幅度的低动量膨胀，散射长度捕获了领先顺序。我们使用仪表/重力双重性计算在强耦合理论中对两个自旋零粒子之间散射长度的主要贡献。我们研究了两种不同的理论，具有质量差距：$ {\ cal n} = 4 $ Super Yang-Mills理论（$ {\ cal n} = 1^*$）的大量变形和一个非超对称的五维理论。这些情况在双重重力描述中对质量差距有不同的认识：前者是众所周知的GPPZ单一解决方案，而后者则是光滑的$ ads_6 $ soliton几何形状。尽管重力双重双重，我们发现散射长度对粒子的质量和创建它们的操作员的共形尺寸具有非常相似的功能依赖性。这在有效描述的有效描述中表现出了普遍的行为，超出了对称性考虑的期望之外的强烈耦合理论。
The low-energy effective theory description of a confining theory, such as QCD, is constructed including local interactions between hadrons organized in a derivative expansion. This kind of approach also applies more generically to theories with a mass gap, once the relevant low energy degrees of freedom are identified. The strength of local interactions in the effective theory is determined by the low momentum expansion of scattering amplitudes, with the scattering length capturing the leading order. We compute the main contribution to the scattering length between two spin-zero particles in strongly coupled theories using the gauge/gravity duality. We study two different theories with a mass gap: a massive deformation of ${\cal N}=4$ super Yang-Mills theory (${\cal N}=1^*$) and a non-supersymmetric five-dimensional theory compactified on a circle. These cases have a different realization of the mass gap in the dual gravity description: the former is the well-known GPPZ singular solution and the latter a smooth $AdS_6$ soliton geometry. Despite disparate gravity duals, we find that the scattering lengths have strikingly similar functional dependences on the masses of the particles and on the conformal dimension of the operators that create them. This evinces universal behavior in the effective description of gapped strongly coupled theories beyond what is expected from symmetry considerations alone.
