AdS3 x S3 x S3 x S1 Hernandel-Lopez相的半经典推导
The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
摘要：
本文利用d（2，1;α）^2代数曲线，用半经典方法计算了AdS 3 x S3 x S3 x S1中弦的Hernan-Lopez相位.通过在一般α下工作，我们包括了以前在AdS 3 x S3 x T4中对该相的半经典计算中没有的模式，特别是可以研究不同质量的粒子的散射。通过对半经典公式的重新推导，我们澄清了AdS_5 × S_5中可以忽略的反对称、截断和表面项等问题，以及AdS_5 × S_5中不存在的c_1，s项等问题。因此，我们看到与最近计算的AdS 3 x S3 x T4情况下的全环修整相位一致，并且对于任何α和任何（光）偏振，在一般情况下AdS 3 x S3 x S3 x S1正好是1/2。
英文摘要：
This note calculates the Hernandez-Lopez phases for strings in AdS3 x S3 x S3 x S1 by semiclassical methods using the d(2,1;α)^2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3 x S3 x T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5 x S5, and some issues about the terms c_1,s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any α and any (light) polarisations.
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