Duality, Generalized Global Symmetries and Jet Space Isometries

Abstract

We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a suitable, possibly graded, target space of fields or its jet space when the theory contains higher derivatives. This is realized via a generalized sigma model perspective motivated from the fact that higher spin particles can be Nambu–Goldstone bosons of spontaneously broken generalized global symmetries. We work out in detail the 2D examples of a compact scalar and the massless Heisenberg pion fireball model and the 4D examples of Maxwell, Born–Infeld, and ModMax electrodynamics. In all cases we identify the ’t Hooft anomaly that obstructs the simultaneous gauging of both global symmetries and confirm the anomaly matching under duality. These results readily generalize to higher gauge theories for p-forms. For multifield theories, we discuss the transformation of couplings under duality as two sets of Buscher rules for even or odd differential forms.

Introductory Notes on Non‐linear Electrodynamics and its Applications

“…$$N=1$$ supersymmetric extensions of ModMax and the generalized Born‐Infeld electrodynamics were constructed in [39, 74], and in [75] ModMax has been generalized to four‐dimensional duality‐invariant (super)conformal non‐linear models of higher‐spin gauge fields. A 't Hooft anomaly in the ModMax theory has been studied in [76].…”

Axial anomaly in nonlinear conformal electrodynamics

“…The latter is described by the recently proposed oneparameter family of Lagrangians dubbed ModMax [53] that includes Maxwell electrodynamics as a particular case. The theory has been studied in the context of black holes, birefringence, supersymmetry, gravitational instantons, wormholes and the 't Hooft anomaly, among other applications [54][55][56][57][58][59][60].…”