Exact Stress Tensor Flows in Causal Electrodynamics: Auxiliary Field Formalism
Abstract
Causal self-dual nonlinear electrodynamics admits a simple auxiliary-field description: the Lagrangian is linear in the two Lorentz invariants of the field strength, and the dynamics is encoded in a potential W(φ) of a single auxiliary variable. We study non-perturbative TT̅-like flows of these theories in this formalism. The irrelevant (stress-tensor) deformation acts on the potential by a rescaling, while the marginal ModMax-type deformation translates its vacuum. We derive the resulting flow equations exactly, show that the irrelevant exact TT̅-like flow takes the autonomous form ∂λℒ=X F(r), where the closed form kernel F depends only on the ratio r=−Tμμ/√(4X−Y) of stress-tensor invariants. We also give an explicit reconstruction of the auxiliary potential from a given kernel. Causality imposes the differential inequality D(r)>1/(1−r), while a globally single-valued kernel requires the ratio r to be monotonic along the auxiliary branch. We examine the relation between the evenness of the exact TT̅-like flow , the φ-parity of the potential, and the analyticity of the Lagrangian in the electromagnetic invariants, including the effect of a marginal ModMax parameter. We construct the linear auxiliary and Hamiltonian formulations and show that the Hamiltonian flow is governed by the same exact TT̅-like flow with the opposite sign. We also express Born's Legendre self-duality, the two characteristic cones, and the energy conditions in terms of the kernel. In particular, r=(ε−p⊥)/(ε+p⊥) has a direct physical interpretation. Exact TT̅-like flow s are obtained for generalized Born-Infeld, logarithmic, q-deformed, and no-τ-maximum electrodynamics.
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BibTeX
@misc{pezhman2026exact,
title = {{Exact Stress Tensor Flows in Causal Electrodynamics: Auxiliary Field Formalism}},
author = {Zahra Pezhman and H. Babaei-Aghbolagh and Komeil Babaei Velni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35135},
eprint = {2610.35135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35135},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Stress Tensor Flows in Causal Electrodynamics: Auxiliary Field Formalism
AU - Zahra Pezhman
AU - H. Babaei-Aghbolagh
AU - Komeil Babaei Velni
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35135
UR - https://arxiv.org/abs/2610.35135
AB - Causal self-dual nonlinear electrodynamics admits a simple auxiliary-field description: the Lagrangian is linear in the two Lorentz invariants of the field strength, and the dynamics is encoded in a potential W(φ) of a single auxiliary variable. We study non-perturbative TT̅-like flows of these theories in this formalism. The irrelevant (stress-tensor) deformation acts on the potential by a rescaling, while the marginal ModMax-type deformation translates its vacuum. We derive the resulting flow equations exactly, show that the irrelevant exact TT̅-like flow takes the autonomous form ∂_λℒ=X F(r), where the closed form kernel F depends only on the ratio r=−T^μ_μ/√(4X−Y) of stress-tensor invariants. We also give an explicit reconstruction of the auxiliary potential from a given kernel. Causality imposes the differential inequality D(r)>1/(1−r), while a globally single-valued kernel requires the ratio r to be monotonic along the auxiliary branch. We examine the relation between the evenness of the exact TT̅-like flow , the φ-parity of the potential, and the analyticity of the Lagrangian in the electromagnetic invariants, including the effect of a marginal ModMax parameter. We construct the linear auxiliary and Hamiltonian formulations and show that the Hamiltonian flow is governed by the same exact TT̅-like flow with the opposite sign. We also express Born's Legendre self-duality, the two characteristic cones, and the energy conditions in terms of the kernel. In particular, r=(ε−p_⊥)/(ε+p_⊥) has a direct physical interpretation. Exact TT̅-like flow s are obtained for generalized Born-Infeld, logarithmic, q-deformed, and no-τ-maximum electrodynamics.
ER -