Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$

Abstract

We present a systematic study of $\mathcal{N}=(2,2)$ supersymmetric non-linear sigma models on $S^2$ 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 $S^2$. 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.

arXiv comment51 pages, refs added

References in corpus (20)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Localization techniques in quantum field theories
• Exact Results in D=2 Supersymmetric Gauge Theories
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Sphere Partition Functions and the Zamolodchikov Metric
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Anomalies, Conformal Manifolds, and Spheres
• Generalized Kahler manifolds and off-shell supersymmetry
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures
• Perturbative Corrections to Kahler Moduli Spaces
• Twisting with a Flip (the Art of Pestunization)
• Gauge Theory Dynamics and Kahler Potential for Calabi-Yau Complex Moduli
• Supersymmetric localization in two dimensions
• Introduction to localization in quantum field theory
• Transversally Elliptic Complex and Cohomological Field Theory
• Twisting gauged non-linear sigma-models
• Gromov-Witten invariants and localization
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$

Cited by in corpus (1)

• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$