First order formulation of the Yang–Mills theory in a background field

Brandt, F. T.; Frenkel, Jacob A.; McKeon, D. G. C.

doi:10.1016/j.aop.2019.167932

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…(A10) yield explicit expressions for the 1PI Green's functions in the loop expansions [68] (though on occasion the loop expansion and an expansion in powers of do not match [69]). Having terms linear in φ i cancel in (A10) complicates the BRST identities to prove renormalizability of gauge theories [70,71]. However, having a background field can be advantageous in gauge theories, as one can chose a gauge fixing condition that retains gauge invariance in the background field.…”

Section: Appendix A: the Background Fieldmentioning

confidence: 99%

Use of Lagrange multiplier fields to eliminate multiloop corrections

et al. 2019

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The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms that are higher-order in the curvature to the action, or invoking compactification of superstring theory from ten to four dimensions. An alternative to these approaches is to introduce a Lagrange multiplier field that restricts the path integral to field configurations that satisfy the classical equations of motion; this has the effect of doubling the usual one-loop contributions and of eliminating all effects beyond one loop. We show how this reduction of loop contributions occurs and find the gauge invariances present when such a Lagrange multiplier is introduced into the Yang-Mills and Einstein-Hilbert actions. Moreover, we quantize using the path integral, discuss the renormalization, and then show how Becchi-Rouet-Stora-Tyutin (BRST) invariance can be used to both demonstrate that unitarity is retained and to find BRST relations between Greens functions. In the Appendices we show how background field quantization can be implemented, consider the use of a Lagrange multiplier field to restrict higher-order contributions in supersymmetric theories, and derive the BRST equations satisfied by the generating functional.

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Section: Appendix A: the Background Fieldmentioning

confidence: 99%

Use of Lagrange multiplier fields to eliminate multiloop corrections

et al. 2019

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“…This simplifies the computations of the quantum corrections in the standard second-order gauge theories, which involve momentum-dependent three-point as well as higher-point vertices. It is well known that the first-order formulation may be achieved by introducing, for example in the Yang-mills theory, an auxiliary field F a µν [1][2][3][4][5][6][7][8][9]. The corresponding first-order Lagrangian density may be written as…”

Section: Introductionmentioning

confidence: 99%

“…From this it follows that L = −1/4f a µν f a µν , which corresponds to the usual second-order Lagrangian. At the quantum level, the renormalization of the first-order formalism has been previously studied from various points of view [1][2][3][4][5][6][7][8][9]. In particular, the BRST renormalization of this formulation has been addressed in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Consistency conditions for the first-order formulation of Yang-Mills theory

et al. 2020

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We examine the self-consistency of the first-order formulation of the Yang-Mills theory. By comparing the generating functional Z before and after integrating out the additional field F a µν , we derive a set of structural identities that must be satisfied by the Green's functions at all orders. These identities, which hold in any dimension, are distinct from the usual Ward identities and are necessary for the internal consistency of the first-order formalism. They relate the Green's functions involving the fields F a µν , to Green's functions in the second-order formulation which contain the gluon strength tensor f a µν . In particular, such identities may provide a simple physical interpretation of the additional field F a µν .

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“…The first order formulation of gauge theories has a simple form involving only cubic interactions, which are momentum-independent. This simplifies the computations of the quantum corrections in the usual second-order gauge theories, that involve momentum dependent three-point as well as higher-point vertices [1][2][3][4][5][6][7][8][9][10][11][12]. In quantum gravity, for example, the first order formulation allows to replace an infinite number of complicated multiple graviton couplings present in the second-order Einstein-Hilbert (EH) action, by a small number of simple cubic vertices [7,8].…”

Section: Introductionmentioning

confidence: 99%

Structural identities in the first order formulation of quantum gravity

Brandt,

Frenkel,

Martins-Filho

et al. 2020

Preprint

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We study the self-consistency of the first order formulation of quantum gravity, which may be attained by introducing, apart from the graviton field, another auxiliary quantum field. By comparing the forms of the generating functional Z before and after integrating out the additional field, we derive a set of structural identities which must be satisfied by the Green's functions at all orders. These are distinct from the usual Ward identities, being necessary for the self-consistency of the first order formalism. They relate the Green's functions involving the additional quantum field to those containing a certain composite graviton field, which corresponds to its classical value. Thereby, the structural identities lead to a simple interpretation of the auxiliary field.

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First order formulation of the Yang–Mills theory in a background field

Cited by 4 publications

References 36 publications

Use of Lagrange multiplier fields to eliminate multiloop corrections

Use of Lagrange multiplier fields to eliminate multiloop corrections

Consistency conditions for the first-order formulation of Yang-Mills theory

Structural identities in the first order formulation of quantum gravity

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