Localizing non-linear sigma model on

Victor Alekseev; Guido Festuccia; Victor Mishnyakov; Nicolai Terziev; Maxim Zabzine

doi:10.1140/epjc/s10052-022-10610-8

2022 Impact factor 4.4

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 766
https://doi.org/10.1140/epjc/s10052-022-10610-8

Regular Article - Theoretical Physics

Localizing non-linear sigma model on

Victor Alekseev¹^,2^,5, Guido Festuccia⁶, Victor Mishnyakov¹^,2^,3^,4, Nicolai Terziev²^,3 and Maxim Zabzine⁶^e

¹ MIPT, 141701, Dolgoprudny, Russia
² NRC “Kurchatov Institute”, 117218, Moscow, Russia
³ Lebedev Physics Institute, 119991, Moscow, Russia
⁴ ITMP, MSU, 119991, Moscow, Russia
⁵ IITP, 127994, Moscow, Russia
⁶ Department of Physics and Astronomy, Uppsala University, Box 516, 75120, Uppsala, Sweden

^e Maxim.Zabzine@physics.uu.se

Received: 12 March 2022
Accepted: 17 July 2022
Published online: 30 August 2022

Abstract

We present a systematic study of supersymmetric non-linear sigma models on with the target being a Kähler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a U(1) action on . In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

© The Author(s) 2022

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