On non-linear chiral 4-form theories in D=10

TL;DR

This work analyzes non-linear, duality-invariant theories of a chiral 4-form in $D=10$, highlighting a vast invariant structure from the self-dual 5-form and showing that the familiar stress-tensor (root-$T\overline{T}$) deformation picture from $D=4,6$ does not generically extend to ten dimensions. Using the INZ framework (generalizing PST with an auxiliary self-dual $\Lambda_5$ and PST scalar $a$) and its equivalence to PST and the clone formulation, the authors derive how the non-linear self-duality and energy-momentum tensor depend on a large set of invariants, especially $I_4$, $I_6$, $I_8$, and beyond. They study ModMax-like conformal deformations with $\mathcal{V}(I_4)$, revealing that the resulting $10D$ energy-momentum tensor contains higher-order invariants such as $I_8$ and $I_{12}$ and that the corresponding flow deviates from a simple root-$T\overline{T}$ form. The paper also establishes the (nontrivial) equivalence between INZ and clone formulations and clarifies the status of the Białynicki-Birula theory as an exception, outlining implications for higher-dimensional duality-invariant theories and possible connections to type IIB string theory.

Abstract

We consider properties of non-linear theories of a chiral 4-form gauge field $A_4$ in ten space-time dimensions with an emphasis on a subclass of these theories which are invariant under the $D = 10$ conformal symmetry. We show that general results regarding a peculiar structure of duality-invariant abelian gauge theories in four and six space-time dimensions do not extend to non-linear chiral 4-form theories in ten dimensions. This discrepancy arises primarily from the large number 81 of independent invariants constructible from the self-dual part of the five-form field strength $F_5=dA_4$ in $D=10$, in stark contrast to the single independent (fourth-order) invariants which are building blocks of the actions in the lower dimensional cases. In particular, unlike the $D=4$ and $D=6$ cases, where non-linear duality-invariant theories can be viewed as stress-tensor ($T\overline T$-like) deformations of seed theories, the flow equations in $D=10$ generally involve both stress-tensor invariants and additional higher-order structures constructed from $F_5$. In passing, we prove the equivalence of three Lagrangian formulations of non-linear duality-invariant $p$-form theories: the PST, the Ivanov-Nurmagambetov-Zupnik and the ``clone" one.