Root-$$ T\overline{T} $$ deformations on causal self-dual electrodynamic theories
H. Babaei-Aghbolagh, Komeil Babaei Velni, Song He, Zahra Pezhman
Abstract
A bstract 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 $$ \frac{\partial \ell }{\partial \tau}\ge 1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>τ</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:math> and $$ \frac{\partial^2\ell }{\partial {\tau}^2}\ge 0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>∂</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∂</mml:mi> <mml:msup> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mfrac> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:math> . 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- $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics.