On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

I. L. Buchbinder; A. S. Budekhina; B. S. Merzlikin

doi:10.1140/epjc/s10052-022-09990-8

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 19
https://doi.org/10.1140/epjc/s10052-022-09990-8

Regular Article - Theoretical Physics

On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

I. L. Buchbinder¹^,2^,3, A. S. Budekhina¹^,2 and B. S. Merzlikin¹^,3^c

¹ Center for Theoretical Physics, Tomsk State Pedagogical University, 634061, Tomsk, Russia
² National Research Tomsk State University, 634050, Tomsk, Russia
³ Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia

^c merzlikin@tspu.edu.ru

Received: 3 November 2021
Accepted: 3 January 2022
Published online: 10 January 2022

Abstract

We study the quantum structure of four-dimensional $N = 2$ ${{\mathcal {N}}}=2$ superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $ω$ $\omega$ . The model is described by harmonic superfield sigma-model metric $g_{ab} (ω)$ $g_{ab}(\omega )$ and two potential-like superfields $L_{a}^{+ +} (ω)$ $L^{++}_{a}(\omega )$ and $L^{(+ 4)} (ω)$ $L^{(+4)}(\omega )$ . In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly $N = 2$ ${{\mathcal {N}}}=2$ supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary $g_{ab} (ω), L_{a}^{+ +} (ω), L^{(+ 4)} (ω)$ $g_{ab}(\omega ), L^{++}_{a}(\omega ), L^{(+4)}(\omega )$ , where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the $N = 2$ ${{\mathcal {N}}}=2$ SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

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