Cubic interactions of d4 irreducible massless higher spin fields within BRST approach

I. L. Buchbinder; V. A. Krykhtin; T. V. Snegirev

doi:10.1140/epjc/s10052-022-10981-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 1007
https://doi.org/10.1140/epjc/s10052-022-10981-y

Regular Article - Theoretical Physics

Cubic interactions of d4 irreducible massless higher spin fields within BRST approach

I. L. Buchbinder¹^,2^,3, V. A. Krykhtin¹^,2 and T. V. Snegirev¹^,2^,4^c

¹ Center of Theoretical Physics, Tomsk State Pedagogical University, 634061, Tomsk, Russia
² National Research Tomsk State University, 634050, Tomsk, Russia
³ Lab. for Theor. Cosmology, International Center of Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia
⁴ Laboratory of Applied Mathematics and Theoretical Physics, TUSUR, Lenin Ave. 40, 634050, Tomsk, Russia

^c snegirev@tspu.edu.ru

Received: 5 October 2022
Accepted: 30 October 2022
Published online: 9 November 2022

Abstract

We develop an approach to constructing the manifestly Lorentz covariant cubic interaction vertices for the four-dimensional massless higher spin bosonic fields with two-component dotted and undotted spinor indices. Such fields automatically satisfy the traceless conditions what simplify form of the equations determining the irreducible massless representation of the Poincaré group with given helicity. The cubic vertex is formulated in the framework of the BRST approach to higher spin field theory. Use of the above spin-tensor fields allows to simplify a form of the BRST-charge and hence to find the cubic vertices just in terms of irreducible higher spin fields. We derive an equation for the cubic vertex and find solutions for arbitrary spins $s_{1}, s_{2}, s_{3}$ $$s_1,s_2,s_3$$ with the number of derivatives $s_{1} + s_{2} + s_{3}$ $$s_1+s_2+s_3$$ in the vertex. As an example, we explicitly construct a vertex corresponding to the interaction of a higher spin field with scalars.

© The Author(s) 2022

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