
arXiv: 1603.08334
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4, 5 and 6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.
33 pages. Forthcoming in: Studies in History and Philosophy of Modern Physics. This is an expanded version of the paper, "On the Relation between Dualities and Gauge Symmetries", which is forthcoming in Philosophy of Science (PSA2014 Proceedings)
High Energy Physics - Theory, gauge/gravity duality, Physics, Physics - History and Philosophy of Physics, Gauge/gravity duality, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 530, General Relativity and Quantum Cosmology, Yang-Mills and other gauge theories in quantum field theory, gauge symmetries, High Energy Physics - Theory (hep-th), Gauge symmetries, Yang-Mills and other gauge theories in mechanics of particles and systems, Dualities, History and Philosophy of Physics (physics.hist-ph), dualities, Gravitational interaction in quantum theory
High Energy Physics - Theory, gauge/gravity duality, Physics, Physics - History and Philosophy of Physics, Gauge/gravity duality, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 530, General Relativity and Quantum Cosmology, Yang-Mills and other gauge theories in quantum field theory, gauge symmetries, High Energy Physics - Theory (hep-th), Gauge symmetries, Yang-Mills and other gauge theories in mechanics of particles and systems, Dualities, History and Philosophy of Physics (physics.hist-ph), dualities, Gravitational interaction in quantum theory
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