Stress Tensor flows, birefringence in non-linear electrodynamics and supersymmetry

Abstract

We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a 4d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> version of the T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence - Born-Infeld, Plebanski, and reverse Born-Infeld - all of which admit ModMax-like generalizations using a root- T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> -like flow that we analyse in our paper. We demonstrate one way of making this root- T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> -like flow manifestly supersymmetric by writing the deforming operator in \mathcal{N} = 1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>𝒩</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> superspace and exhibit two examples of superspace flows. We present scalar analogues in d = 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> with similar properties as these theories of electrodynamics in d = 4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . Surprisingly, the Plebanski-type theories are fixed points of the classical T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> -like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related “subtracted” theory for which the stress-tensor-squared operator is a constant.

Topics & Concepts