Abstract
Nontrivial Bianchi identities with local magnetic sources are solved by recognizing that gauge potentials are sections rather than globally defined functions, but properly accounting for the source degrees of freedom requires a modification of the field strength. Following work by Teitelboim and by Cariglia and Lechner, we extend Dirac's string formalism for monopoles to D-branes in type IIA and IIB string theory. We give novel derivations of brane-induced Chern-Simons terms in the supergravity actions, including a prescription for integrating over potentials in the presence of magnetic sources. We give a noncovariant formulation of the IIB theory, keeping only the independent degrees of freedom of the self-dual 4-form potential. Finally, it is well-known that D8-branes source the mass parameter of IIA supergravity; we show that the additional couplings of the massive IIA supergravity, including on other D-brane worldvolumes, are a consequence of the corresponding Dirac branes.
Highlights
In modern mathematical treatments, we recognize the vector potential of a gauge theory not as a globally defined function but as the section of a gauge fiber bundle [1,2]
We propose that additional WZ couplings on D-branes in the massive theory [25,26] are a consequence of the Dirac brane currents and conjecture the presence of other new WZ couplings on type IIA D-branes
We consider a set of potentials Cpþ1 and corresponding gauge-invariant field strengths Fpþ2, with an additional set of field strengths Hrþ1 1⁄4 dBr assumed closed with pullbacks 1⁄2Hrþ1 that appear in dG for some branes
Summary
We recognize the vector potential of a gauge theory not as a globally defined function but as the section of a gauge fiber bundle [1,2]. Gauge patching allows the description, for example, of a constant magnetic field strength on a torus (the distinct patches cover different unit cells) or the field of a magnetic monopole (where the Bianchi identity dF2 ≠ 0 can have no globally defined solution) Analogs of both these examples for higher-rank form potentials are important in string theory as harmonic background flux in compactifications and higher-dimensional D-branes (and NS5branes) that carry magnetic charges for the fundamental potentials. An alternative that displays the coupling of magnetic sources explicitly is to double the number of gauge degrees of freedom by introducing dual field strengths and corresponding potentials. A forthcoming companion paper [27] will demonstrate how Dirac’s formalism separates the brane and gauge degrees of freedom in a form useful for dimensional reduction
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