Self-dual instantons and gravitating dyons in non-Abelian ModMax theory

Abstract

Motivated by the recent interest in conformal and duality invariant nonlinear electrodynamics, we study the non-Abelian extension of ModMax electrodynamics. The theory is parameterized by a single dimensionless constant, and it is continuously connected to Yang-Mills theory in its vanishing limit. We show that the theory admits (anti-)self-dual instantons, despite the additional nonlinearities that characterize the non-Abelian ModMax theory. For $SU(2)$, we construct the generalization of the BPST instanton and extend this solution to Euclidean de Sitter and anti-de Sitter backgrounds. In the latter case, the Chern-Pontryagin index depends on the instanton size since the configuration is not a pure gauge at infinity; a property already pointed out in Yang-Mills on negative-curvature backgrounds by Callan and Wilczek. We compute the contribution of the latter to the spectrum of the Dirac operator at the boundary, which is crucial for determining the non-local contributions to the Dirac index. Then, we show that the ansatz constructed with 't Hooft symbols accommodates multi-instantons in the non-Abelian ModMax theory. The system of (anti-)self-dual equations reduces to a single nonlinear equation, which can be perturbatively solved order by order in the parameter that controls the nonlinearity. Following such a strategy, we provide a formal solution for the $N$-instanton configuration to first order in the expansion. Then, we couple non-Abelian ModMax theory to gravity with a conformally coupled scalar field and construct new gravitating solutions that describe Euclidean wormholes and other smooth configurations with secondary hair.

v1: 21 pages; v2: 22 pages. References and comments added. Accepted for publication in JHEP

References in corpus (28)

• Static wormhole solution for higher-dimensional gravity in vacuum
• Introductory Notes on Non-linear Electrodynamics and its Applications
• Euclidean Wormholes in String Theory
• Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns
• Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter
• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Accelerated Black Holes beyond Maxwell's Electrodynamics
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Entanglement entropy in three dimensional gravity
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Thermodynamic geometry and complexity of black holes in theories with broken translational invariance
• Electromagnetized black holes and swirling backgrounds in nonlinear electrodynamics: The ModMax case
• AdS-Taub-NUT spacetimes and exact black bounces with scalar hair
• Exact rotating wormholes via Ehlers transformations
• Black-hole solution in nonlinear electrodynamics with the maximum allowable symmetries
• Plebanski-Demianski solutions in Quadratic gravity with conformally coupled scalar fields
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Axion wormholes with massive dilaton
• Finite-action solutions of Yang-Mills equations on de Sitter dS${}_4$ and anti-de Sitter AdS${}_4$ spaces
• Nonlinearly charging the conformally dressed black holes preserving duality and conformal invariance
• Exact multiblack hole spacetimes in Einstein-ModMax theory
• Wormholes and entanglement in holography
• Non-Abelian Wormholes Threaded by a Yang-Mills-Higgs Field beyond the BPS Limit
• Axial anomaly in nonlinear conformal electrodynamics
• Euclidean AdS wormholes and gravitational instantons in the Einstein-Skyrme theory
• Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory