On the symmetry foundation of double soft theorems

Abstract

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

Matter couplings and equivalence principles for soft scalars

“…These are the analogues of Weinberg's soft graviton theorem [17,69] and are well-known for the pure scalar theories [26][27][28], 9 but here we see that they hold also in the presence of matter.…”

“…From this factorized statement, the additional information that is analogous to the on-shell Ward identity is the demand that the universal soft factor satisfies the appropriate single-soft theorem. Similar to the subleading single soft theorems enjoyed by gravity [18][19][20], the DBI and special galileon theories also satisfy subleading double soft theorems [26][27][28]. We verify that these subleading double soft theorems continue to hold in the presence of matter couplings, while the sub-subleading theorems are not universal.…”

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

“…These theorems (and its generalization to the multiple soft graviton case) have been studied previously using various methods including BCFW recursions [31], CHY amplitudes [32][33][34][35] and Feynman diagram techniques [24]. In a recent work [36], the authors have studied the symmetry foundations of the double soft theorems of certain classes of theories like the dilaton, DBI, and special Galileon.…”

Quantum corrections to generic branes: DBI, NLSM, and more

“…• Are constructible via soft-bootstrap methods, due to their "exceptional" soft-scaling behavior [8][9][10][11] • Exhibit non-trivial single-and double-soft limits inherited from non-linear symmetries [12][13][14][15][16][17][18][19][20][21][22][23] • Belong to the handful of theories which appear in double-copy relations [24] • Admit CHY representations [25,26] The preceding references are only a partial list and many straddle the different categories above.…”