Conformally soft fermions

Abstract

Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin s = $$ \frac{1}{2} $$ 1 2 and $$ \frac{3}{2} $$ 3 2 conformal primary wavefunctions with definite SL(2, ℂ) conformal dimension ∆ and spin J where |J| ≤ s. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with ∆ = $$ \frac{1}{2} $$ 1 2 and its shadow with ∆ = $$ \frac{3}{2} $$ 3 2 which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.

Goldilocks Modes and the Three Scattering Bases

“…In [16] we established how to analytically continue the bulk conformal primary wavefunctions Φ ǫ ∆,J off the principal series to capture conformally soft modes and demonstrated that the operators defined via the inner-product dictionary O ǫ ∆,J = i( Ôs , (Φ −ǫ ∆,J ) * ) (1.6) correspond to the anticipated soft charges in each instance of a known asymptotic symmetry (large U(1), supertranslations, superrotations) in gauge theory and gravity (s = 1, 2) at the expected integer values of ∆. This was extended to the supergravity case in [17]. The operators O ∆,J indeed become the canonical charge for a corresponding asymptotic symmetry whenever the wavefunctions Φ ∆,J is pure gauge [16], which is the case for 1 − s < ∆ ≤ 1, and we refer to them as Goldstone wavefunctions.…”

“…The inner product (2.22) serves to project out the polarization tensors, so that the operator O − ℓ (ω, w, w) is just the annihilation operator a ℓ (ω, w, w). This is particularly useful for the half-integer spin case [17]. We can then use the transforms (2.1) and (2.3) to go to the other bases.…”

“…We now turn to the question of identifying the Goldstone and memory modes in the celestial basis. Energetically and conformally soft theorems have been related to asymptotic symmetries in [34,35,[76][77][78] and [6,[16][17][18]79]. These are the residual gauge transformations that are consistent with the conformal primary gauge fixing.…”

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

“…In [8], the supersymmetric w 1+∞ algebra has been identified with the corresponding soft current algebra in the supersymmetric Einstein-Yang-Mills theory. The relevant works on the celestial holography in the various directions can be found in [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. See [1] for more complete literatures.…”

Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries

“…Finally, a new understanding of the gravitational renormalization procedure connecting finite to asymptotic surfaces has been achieved [17,19,53,64]. On the celestial side, some of the highlights include the reformulation of scattering amplitudes into a basis of asymptotic boost eigenstates [23,24,[65][66][67], an ever-growing catalogue of celestial symmetries [31,33,[68][69][70][71][72][73][74][75][76][77] and their associated constraints [32,[34][35][36]78], as well as a framework amenable to the use of standard conformal field theory (CFT) methods [79][80][81][82][83] for gravity in AFS. Intriguingly, a w 1+∞ structure [84][85][86] was recently encountered in the algebra of the infinite tower of conformally soft graviton symmetries [37,38].…”