arXiv 2305.095872023-05hep-thgr-qchep-phmath-phmath.MP

非超对称真空与自伴延拓

Non-Supersymmetric Vacua and Self-Adjoint Extensions

J. Mourad, A. Sagnotti

备注：: 49 pages, LaTeX, 13 figures. References added, misprints corrected in eqs. (3.71) and (3.72). Final version to appear in JHEP (with some additional misprints removed while correcting the proofs)

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AI总结：

本文研究破缺超对称弦紧致化中区间端点奇点处薛定谔算符的自伴延拓，并将其应用于 tadpole 势驱动的 orientifold 真空，在九维中确定了稳定张量模式和无质量引力子对应的唯一边界条件选择。

摘要：

由共形坐标 $z$ 的有限区间张成并终止于一对奇点的内部区间，是许多破缺超对称的弦紧致化的共同特征。在低维闵可夫斯基时空中出现的平方质量于是成为类薛定谔算符的本征值，这些算符的势在区间端点处具有双极点。对于单分量系统，薛定谔算符的可能自伴延拓由 $AdS_3 \times S^1$ 中的点描述，而与区间端点处独立边界条件相对应的自伴延拓则由 $AdS_3$ 边界上的点描述。紧致化到闵可夫斯基时空的微扰稳定性通常取决于这些自伴延拓的选择。我们将这一框架应用于由“tadpole 势” $V=T \\ e^{\\,\frac{3}{2}\\,\phi}$ 驱动的 orientifold 真空，并发现在九维中存在一个有大质量标量谱、具有稳定张量模式和无质量引力子的唯一边界条件选择，以及多种可导致无质量和/或有质量矢量模式的选择。

英文摘要：

Internal intervals spanned by finite ranges of a conformal coordinate $z$ and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in $AdS_3 \times S^1$, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of $AdS_3$. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the ``tadpole potential'' $V=T \ e^{\,\frac{3}{2}\,ϕ}$ and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.

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