The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an auxiliary field, τ, and Courant-Hilbert functions, ℓ(τ), which depend on τ. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mrow> <mi>∂</mi> <mi>ℓ</mi> </mrow> <mrow> <mi>∂</mi> <mi>τ</mi> </mrow> </mfrac> <mo>≥</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$ \frac{\partial \ell }{\partial \tau}\ge 1 $</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mrow> <msup> <mi>∂</mi> <mn>2</mn> </msup> <mi>ℓ</mi> </mrow> <mrow> <mi>∂</mi> <msup> <mi>τ</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>≥</mo> <mn>0</mn> </math></EquationSource> <EquationSource Format="TEX">$ \frac{\partial^2\ell }{\partial {\tau}^2}\ge 0 $</EquationSource> </InlineEquation>.In this paper, we investigate theories with two coupling constants that also comply with the principle of causality. We demonstrate that these theories possess a new universal representation of the root-<InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ T\overline{T} $</EquationSource> </InlineEquation> operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics.

Root-$ T\overline{T} $ deformations on causal self-dual electrodynamic theories

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2025年7月22日

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H. Babaei-Aghbolagh,
Komeil Babaei Velni,
Song He,
Zahra Pezhman

摘要

The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an auxiliary field, τ, and Courant-Hilbert functions, ℓ(τ), which depend on τ. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions $\frac{\partial ℓ}{\partial τ} \geq 1$ $ \frac{\partial \ell }{\partial \tau}\ge 1 $ and $\frac{\partial^{2} ℓ}{\partial τ^{2}} \geq 0$ $ \frac{\partial^2\ell }{\partial {\tau}^2}\ge 0 $ .

In this paper, we investigate theories with two coupling constants that also comply with the principle of causality. We demonstrate that these theories possess a new universal representation of the root- $T \bar{T}$ $ T\overline{T} $ operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics.

Root-\( T\overline{T} \) deformations on causal self-dual electrodynamic theories

摘要