Crossing antisymmetric Polyakov blocks + Dispersion relation

Abstract

Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the '+ type Polyakov blocks'. These blocks are built from AdS d+1 Witten diagrams. In 1d they encode the '+ type' analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent 'locality constraints' in addition to the usual CFT sum rules given by the 'Polyakov conditions'. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

Locality and Analyticity of the Crossing Symmetric Dispersion Relation

“…• An exciting application will be to explore our discussion in the context of the CFT correlators of charged fields discussed in [46] and the functionals therein also to [47,48].…”

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

“…See also[29,46] for crossing symmetric/ Anti-Symmetric kernels in context of CFT bootstrap 9. There can be multiple such amplitudes associated with a given scattering when the particles have extra quantum numbers such as spin, isospin e.t.c10 We are considering both s and t as complex variables.…”

Mixed Correlator Dispersive CFT Sum Rules

“…In recent years, with the introduction of analytic functionals [20][21][22][23][24][25][26][27] and dispersion relation methods [28][29][30][31][32][33][34], the gap between numerics and analytics has greatly narrowed revealing new horizons for the bootstrap program. This paper builds upon this bridge by introducing new analytic dispersive functionals for correlators with unequal external scalar operators.…”