2D Kac-Moody symmetry of 4D Yang-Mills theory

Abstract

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CP T invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.

Double-soft limits of gluons and gravitons

“…The authors of [5] moreover related the subleading soft graviton functions to a conjectured hidden symmetry of the quantum gravity S-matrix [6,7] which has the form of an extended BMS 4 algebra [8][9][10] known from classical gravitational waves. Similar claims that the Yang-Mills S-matrix enjoys a hidden two-dimensional Kac-Moody type symmetry were made recently [11]. In this picture the scattering amplitudes in four-dimensional quantum field theory are related to correlation functions of a two-dimensional quantum theory living on the sphere at null infinity.…”

Asymptotic symmetries, holography and topological hair

“…9 Emergent CS and "shadow" effects from boundary/soft limits In Mink 4 gauge theory, it was shown that AS and memory effects arise from considering same-helicity gauge boson emissions in the soft limit [6,7]. Ref.…”

“…Considerable progress has been made in this regard by the discovery that the associated large diffeomorphisms and gauge transformations arise as soft limits of physical gravitational and gauge fields emerging from scattering processes [5][6][7][8][9][10][11][12][13][14][15], as captured by the Weinberg Soft Theorems [16][17][18][19][20]. The infinite-dimensional AS then describe the soft field dressing of a hard process, and are sensitive to the passage of charge/energy-momentum as a function of angle, through "memory" effects [21][22][23][24][25][26][27][28][29][30].…”

On soft theorems and form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory

“…The corresponding Ward identities are equivalent to gauge theory soft theorems [19,20]. Moreover, it was shown, that scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity [20].…”