平直11维背景下环形M2膜的能量
Energy of toroidal M2 brane in flat 11d background
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中文总结 AI 辅助
针对超膜作用量非线性且先验不可重整的问题，通过逆张力展开计算平直11维空间中绕2-环面的M2膜能量至两圈，验证其无对数紫外发散，还计算玻色膜三圈修正并求和全圈气泡图得到能量的三次方程，探讨相关理论关联猜想。
中文摘要 AI 辅助
超膜作用量是非线性的，且先验上不可重整。不过，该理论中的某些物理量可能不存在对数紫外发散，因而可以被明确地定义。为探究这一可能性，我们通过逆张力展开，计算了平直11维空间中缠绕在2-环面上的M2膜的两圈能量。计算结果不存在对数发散，且在更高圈阶下也应保持这一性质。对于沿两个圆周方向均取周期性边界条件的费米子，量子修正会相互抵消，这与缠绕M2膜态的BPS性质相符。对于沿一个或两个圆周方向取反周期性边界条件的费米子，其能量是半径的非平凡函数，由修正贝塞尔函数的无穷求和给出。我们还计算了$\mathbb R^2\times S^1$上玻色膜能量的三圈修正。与弦论情形不同的是，除了一圈$ζ(3)$系数的幂次项之外，它还包含一个与$ζ(9)$成正比的新项。对全圈气泡图的贡献求和后，我们得到了膜能量满足的一个简单三次方程。在Nambu弦或GS弦情形下进行的类似重整化求和，可重现我们熟知的精确平方根表达式${\mathcal E}=\sqrt{(2πR\,T_1)^2+m_0^2}$。我们发现，对于任意半径$R_{11}$，膜能量的气泡图部分都不会为零。如果超膜情形下其他非平凡图的贡献不会从定性上改变这一结论，那么这将不利于“反周期性圆周上的11维理论与0A型弦论的强耦合极限之间存在关联”这一猜想。
英文摘要
The supermembrane action is non-linear and a priori non-renormalizable. Still, some quantities in this theory may be free of log UV divergences and thus defined unambiguously. To explore this possibility we compute the energy of an M2 brane wrapped on a 2-torus in flat 11d space to two loops in the inverse-tension expansion. The result is free of logarithmic divergences and the same should hold also at higher loop orders. For fermions periodic around both circles the quantum corrections cancel, consistent with the BPS nature of the wrapped M2 brane state. For fermions antiperiodic around one or both circles the energy is a non-trivial function of the radii given by infinite sums of modified Bessel functions. We also compute 3-loop correction to the energy of the bosonic membrane on $\mathbb R^2\times S^1$. In contrast to the string case, it contains, besides powers of the 1-loop $ζ(3)$ coefficient, a new term proportional to $ζ(9)$. Summing contributions of all-loop bubble graphs leads to a simple cubic equation for the membrane energy. The analogous resummation in the Nambu or GS string case reproduces the familiar exact square-root expression ${\mathcal E}=\sqrt{(2πR\,T_1)^2+m_0^2}$. We find that the bubble-graph part of the membrane energy does not vanish for any value of the radius $R_{11}$. If contributions of other non-trivial diagrams in the supermembrane case do not qualitatively change this conclusion, this would disfavour the conjectured relation between 11d theory on an antiperiodic circle and the strong-coupling limit of type 0A string theory.
发表机构
- Imperial College London（伦敦帝国理工学院）
- Institute for Theoretical and Mathematical Physics (ITMP) of MSU（莫斯科国立大学理论与数学物理研究所）
- Lebedev Institute（列别捷夫物理研究所）
- Abdus Salam Centre for Theoretical Physics（阿卜杜斯·萨拉姆理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。
