A new Wilson line-based action for gluodynamics

Kakkad, Hiren; Kotko, Piotr; Staśto, Anna

doi:10.1007/jhep07(2021)187

Cited by 6 publications

(17 citation statements)

References 54 publications

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“…Triple point vertices are not very effective building blocks for calculating amplitudes, and, actually they do not constitute any physical amplitude themselvesin the on-shell limit they are zero (for real momenta). Motivated by the geometric considerations mentioned before and the above arguments we proposed in [8] another set of field transformations that lead to a new action.…”

Section: New Classical Actionmentioning

confidence: 99%

“…The new canonical field transformations are based on path ordered exponentials of the gauge fields, extending over both the self-dual and anti-self-dual planes [8]:…”

Section: Field Transformationmentioning

confidence: 99%

“…In [8] we showed that the transformation (10) is equivalent to two canonical transformations: first transforming the self-dual part of the Yang-Mills action to the kinetic term in MHV action (2), and then transforming the anti-self-dual part in the latter to kinetic term in the new action…”

Section: Field Transformationmentioning

confidence: 99%

“…The new action can be most easily derived [8] by substituting the inverse of Z fields (13) in the MHV action. For a generic Wilson line W (7), the inverse functional, W −1 , is defined using the relation…”

Section: Structure Of the Actionmentioning

confidence: 99%

“…Indeed, in [8], we derived a new classical action for gluodynamics in which the fields are directly related to Wilson line functionals extending over both the self-dual and the anti-self-dual planes. The action is most easily derived through a canonical transformation of the anti-self-dual part of the MHV action, but we also discuss a direct link between the new action and the Yang-Mills action.…”

Section: Introductionmentioning

confidence: 99%

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A new Wilson Line-based classical action for gluodynamics

Kakkad¹,

Kotko²,

Staśto³

2021

Preprint

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We develop a new classical action that in addition to MHV vertices contains also N k MHV vertices, where 1 ≤ k ≤ n − 4 with n the number of external legs. The lowest order vertex is the four-point MHV vertex -there is no three point vertex and thus the amplitude calculation involves fewer vertices than in the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action. The action is obtained by a canonical transformation of the Yang-Mills action in the light-cone gauge, where the field transformations are based on the Wilson line functionals.

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Section: New Classical Actionmentioning

confidence: 99%

“…The new canonical field transformations are based on path ordered exponentials of the gauge fields, extending over both the self-dual and anti-self-dual planes [8]:…”

Section: Field Transformationmentioning

confidence: 99%

Section: Field Transformationmentioning

confidence: 99%

Section: Structure Of the Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new Wilson Line-based classical action for gluodynamics

Kakkad¹,

Kotko²,

Staśto³

2021

Preprint

Self Cite

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One-Loop effective action approach to quantum MHV theory

Kakkad

Kotko

Staśto

2022

J. High Energ. Phys.

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It is well known that the MHV action, i.e. the action containing all the maximally helicity violating vertices, is alone not sufficient for loop computations. In order to develop loop contributions systematically and to ensure that there are no missing terms, we propose to formulate the quantum MHV action via one-loop effective action approach. The quadratic field fluctuations in the light cone Yang-Mills theory are explicitly integrated, followed by the classical canonical field transformation. We test the approach by calculating one loop (++++) and (+++) amplitudes, i.e. amplitudes that cannot be calculated from ordinary MHV action. Such an approach can be further used to unambiguously define loop corrections in other theories related to Yang-Mills theory by field transformations.

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Wilson line-based action for gluodynamics at the loop level

Kakkad,

Kotko,

Stasto

2024

J. High Energ. Phys.

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We develop quantum corrections to the Wilson line-based action which we recently derived through a transformation that eliminates triple gluon vertices from the Yang-Mills action on the light-cone. The action efficiently computes high multiplicity tree-level split-helicity amplitudes with the number of diagrams following the Delannoy number series. However, the absence of the triple gluon vertices results in missing loop contributions. To remedy this, we develop two equivalent approaches using the one-loop effective action method to systematically incorporate loop contributions to our action. In one approach there are solely Yang-Mills vertices in the loop whereas the other uses the interaction vertices of our action along with the kernels of the solution of our transformation in the loop. In addition to demonstrating the equivalence of both approaches, we validated the quantum completeness of the former by computing all 4-point one-loop amplitudes which could not be previously computed. Both of our approaches are easily extendable to develop quantum corrections to other reformulations of the Yang-Mills theory obtained via non-linear classical field transformations eliminating interaction vertices.

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A new Wilson line-based action for gluodynamics

Cited by 6 publications

References 54 publications

A new Wilson Line-based classical action for gluodynamics

A new Wilson Line-based classical action for gluodynamics

One-Loop effective action approach to quantum MHV theory

Wilson line-based action for gluodynamics at the loop level

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