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Comparing Dualities and Gauge Symmetries

De Haro, Sebastian and Teh, Nicholas and Butterfield, Jeremy (2016) Comparing Dualities and Gauge Symmetries. [Preprint]

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Abstract

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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
De Haro, Sebastiansd696@cam.ac.uk
Teh, Nicholasnichoteh@gmail.com
Butterfield, Jeremyjb56@cam.ac.uk
Additional Information: Forthcoming in: Studies in the 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).
Keywords: Dualities, gauge symmetries, gauge/gravity duality, AdS/CFT, theoretical equivalence, the empirical significance of gauge symmetries, Galileo’s ship
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Depositing User: Jeremy Butterfield
Date Deposited: 28 Mar 2016 15:53
Last Modified: 28 Mar 2016 15:53
Item ID: 12009
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Date: 27 March 2016
URI: http://philsci-archive.pitt.edu/id/eprint/12009

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