探索对有效行动的软约束
Exploring soft constraints on effective actions
摘要：
我们研究有效的行动，同时打破时空和内部对称性。新的功能出现，由于混合的戈德斯通模式下打破对称性，与通常的阿德勒的零，导致非零软限制。这种情况对于自发断裂的SCFT是常见的。我们明确测试这些软定理$\mathcal{N}=4$ sYM在库仑分支微扰和非微扰。我们利用递归关系系统地探索软约束。在一般的CFT的纯介子扇区中，我们证明了直到$s^{n} \sim \partial^{2n}$阶的所有振幅完全由$s^k$阶的$k$点振幅和$k \leq n$决定.最多有一个导数作用于每一个DBI的项是完全固定的，并且与共形DBI中出现的项一致，即AdS中的DBI。有了极大超对称性，有效作用量被进一步限制，导致新的非重整化定理。特别地，有效作用量被固定为八个导数，仅用一个未知的四点系数和一个系数来表示十个导数项。最后，我们还研究了在这种情况下规模和共形不变性之间的相互作用。
英文摘要：
We study effective actions for simultaneous breaking of space-time and internal symmetries. Novel features arise due to the mixing of Goldstone modes under the broken symmetries which, in contrast to the usual Adler's zero, leads to non-vanishing soft limits. Such scenarios are common for spontaneously broken SCFT's. We explicitly test these soft theorems for $\mathcal{N}=4$ sYM in the Coulomb branch both perturbatively and non-perturbatively. We explore the soft constraints systematically utilizing recursion relations. In the pure dilaton sector of a general CFT, we show that all amplitudes up to order $s^{n} \sim \partial^{2n}$ are completely determined in terms of the $k$-point amplitudes at order $s^k$ with $k \leq n$. Terms with at most one derivative acting on each dilaton insertion are completely fixed and coincide with those appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry, the effective actions are further constrained, leading to new non-renormalization theorems. In particular, the effective action is fixed up to eight derivatives in terms of just one unknown four-point coefficient and one more coefficient for ten-derivative terms. Finally, we also study the interplay between scale and conformal invariance in this context.
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