Bulk locality for scalars and fermions with global symmetry

Chowdhury, Subham Dutta; Ghosh, Kausik

doi:10.48550/arxiv.2107.06266

“…Our results are hence applicable to these cases (see e.g. [39]). However when fermions or unequal scalars are involved the conformal blocks are different, and also we may lose full crossing (anti)symmetry.…”

mentioning

confidence: 60%

Crossing antisymmetric Polyakov blocks + Dispersion relation

Kaviraj

2021

Preprint

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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.

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“…We can easily write down examples of such functions built out of polynomials of mandelstam invariants [39,45,55].…”

Section: Parity Violating Amplitudesmentioning

confidence: 99%

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Chowdhury

¹

,

Ghosh

²

,

Haldar

³

et al. 2022

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We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

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Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Chowdhury¹,

Ghosh²,

Haldar³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

show abstract

Bulk locality for scalars and fermions with global symmetry

Cited by 3 publications

References 46 publications

Crossing antisymmetric Polyakov blocks + Dispersion relation

Crossing antisymmetric Polyakov blocks + Dispersion relation

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

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