Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics

Abstract

We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\mu \nu }$ replaced by a unit-determinant metric $h_{\mu \nu }(F)$ which is a function of the field strength $F_{\mu \nu }$, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric $h_{\mu \nu }(F)$ produces identical equations of motion when it is coupled to the Maxwell theory via two different prescriptions which we describe. We use the field-dependent metric perspective to analyze the electric and magnetic $1$-form global symmetries in models of self-dual electrodynamics. This analysis suggests that any duality-invariant theory possesses a set of conserved currents $j^{\mu }$ which are in one-to-one correspondence with $2$-forms that are harmonic with respect to the field-dependent metric $h_{\mu \nu }(F)$.

29 pages, contribution to the proceedings for the MATRIX workshop "New Deformations of Quantum Field and Gravity Theories"; v3: final version to be published

References in corpus (26)

• Generalized Global Symmetries
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Introductory Notes on Non-linear Electrodynamics and its Applications
• On p-form gauge theories and their conformal limits
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• An Introduction to Higher-Form Symmetries
• Boosting to BMS
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Self-interacting chiral p-forms in higher dimensions
• Massive gravity generalization of $T\overline{T}$ deformations
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Quantization of the ModMax Oscillator
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• Four-fermion deformations of the massless Schwinger model and confinement
• Waves and strings in an interacting conformal chiral 2-form theory in six dimensions
• Duality, generalized global symmetries and jet space isometries
• Conservation of all Lipkin's zilches from symmetries of the standard electromagnetic action and a hidden algebra