arXiv 1111.66282011-11hep-th

AdS_4 x CP ^3中的字符串：有限大小谱与Bethe Anterior

Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz

Davide Astolfi, Gianluca Grignani, Enrico Ser-Giacomi, A. V. Zayakin

备注：: 32 pages. Published version; journal reference added
发表信息：: JHEP04(2012)005
DOI：: 10.1007/JHEP04(2012)005

摘要：

我们计算了光锥规范IIA型弦论谱的第一曲率修正，它是在$AdS_4\times \mathbb{CP}^3$关于平面波极限的展开中产生的。由此产生的频谱精确匹配，无论是在幅度和退化，相应的解决方案的全循环格罗莫夫-维埃拉贝特Anglomov。取消了能级匹配条件，计算了理论中所有单振子态的单圈色散关系修正。它被证明有所有的对数发散取消，只留下一个有限的指数抑制的贡献，如前所示的轻玻色子。我们认为，有没有模糊的选择的正则化的自能和，因为正则化应用是唯一一个保持酉。计算了全简并双振子扇区中的相互作用矩阵，并完全确定了两个轻磁振子的谱。在双磁振子扇区中，相同的有限尺寸修正，在1/J的数量级，其中$J$是链的长度，计算从所有的回路Bethe Anglomerate。由这两种完全不同的方法得到的修正在$λ' =λ/J^2$中达到四阶。我们推测等价性扩展到$λ$中的所有阶和1/J中的更高阶。

英文摘要：

We compute the first curvature corrections to the spectrum of light-cone gauge type IIA string theory that arise in the expansion of $AdS_4\times \mathbb{CP}^3$ about a plane-wave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the self-energy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate two-oscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finite-size corrections, at the order 1/J, where $J$ is the length of the chain, in the two-magnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in $λ' =λ/J^2$. We conjecture that the equivalence extends to all orders in $λ$ and to higher orders in 1/J.

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英文摘要：

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