On Current-Squared Flows and ModMax Theories

Abstract

We show that the recently introduced ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equation driven by a quadratic combination of stress-energy tensors. The operator associated to this flow is a 4d analogue of the T T deformation in two dimensions. This result generalizes the observation that the ordinary Born-Infeld Lagrangian is related to the free Maxwell theory by a current-squared flow. As in that case, we show that no analogous relationship holds in any other dimension besides d = 4. We also demonstrate that the N = 1 supersymmetric version of the ModMax-Born-Infeld theory obeys a related supercurrent-squared flow which is formulated directly in N = 1 superspace.

Root-$T \overline{T}$ Deformations

“…which is precisely the result obtained in Ref. [23] from the dimensional reduction of the four-dimensional ModMax-Born-Infeld theory [16,17,21,22].…”

“…( 5) admits a T T -like deformation in terms of a Born-Infeld action with parameter λ. The resulting two parameter, four-dimensional action S (λ,γ) is the solution of two commuting flow-equations [20][21][22]. The flows we introduce here precisely generate, and extend, the reduction to two dimensions of the ModMax-Born-Infeld action recently obtained in Ref.…”

“…The study of T T and holography has also led to new irrelevant deformations in D > 2 dimensions [40,41]. Similar stress-energy tensor squared deformations have also emerged as key ingredients in (supersymmetric) four-dimensional Mod-Max [20][21][22]42]. Both our D = 2 operator R, Eq.…”

Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions

“…ModMax theory has been proposed as a unique conformal nonlinear electrodynamics theory, which is a marginal modification on the pure Maxwell theory [22]. We have showed that there exists a marginal T T -like operator in the form of (2.1) in [1], which reproduces the ModMax theory from a pure Maxwell theory (Also, see [23]). we showed that the ModMax as well as generalized Born-Infeld (GBI) 1 Lagrangian density fulfill the flow equations:…”

Note on $T\bar{T}$ deformed matrix models and JT supergravity duals

“…For higherdimensional cases, it has been explored in [14]. For lower dimension, i.e., the one-dimensional case or ordinary quantum mechanic system, which is the main interest of present work, the T T deformation was first introduced in [15,16], see also recent developments [17][18][19][20][21][22][23][24].…”