### Argument

**The ontology of symmetries in physics** has recently been approached from a new perspective: the matching of theoretical symmetries with empirical symmetries. This matching, known under the name of the **direct empirical status** or **direct empirical significance ****(DES)** of theoretical symmetries, is supposed to identify those theoretical symmetries that correspond to genuine symmetries in the world, as opposed to those which do not. The topic has been discussed by Kosso (2000), Brading and Brown (2004), Healey (2009), Greaves and Wallace (2014), Friederich (2015), Teh (2016), and Ladyman and Presnell (manuscript).

**An empirical symmetry** consists in the invariance of observable phenomena under physical transformations. For instance, Galileo's ship empirical symmetry consists in the invariance of the observable movement inside a cabin of a ship under a physical boost of the ship. Faraday's (charged) cage, 't Hooft's (phase-shifted) beam-splitter, Einstein's (free-falling or accelerating) elevator, space translations and space rotations are also taken to be empirical symmetries.

**For a theoretical symmetry** to have a DES it is necessary that it be able to represent an empirical symmetry. Theoretical symmetries of special relativity, electrostatics, classical electromagnetism, quantum mechanics, semi-classical electrodynamics and general relativity have all been claimed to have a DES.

**Establishing a DES is promising** because empirical symmetries involve physical transformations. So theoretical symmetries adequately representing them should be interpreted as describing genuine changes in the world. This opposes theoretical symmetries having a DES to gauge symmetries, usually understood as being redescriptions of the same state of the world. The conclusion applies extensively given that empirical symmetries are numerous and because many physical theories are concerned.

**On the other hand,** the straightforward application of the approach has run into some difficulties. One of them arises whenever both global and local theoretical symmetries are able to represent the same empirical symmetry. Ascribing a physical interpretation to all the theoretical symmetries in this case goes against the usual understanding of local symmetries as gauge symmetries, and fails to yield a substantial ontology given that global and local representations of the same empirical symmetry have little in common. Whether restricting the DES to global symmetries alone is an adequate solution is being discussed.

**An articulation of the DES approach to other approaches** to the ontology of symmetries should also be worked out. For instance, Noether's theorems differently associate global and local symmetries to conservation laws and link local symmetries to indeterminism. Gauge theories suggest ontologies of fields or holonomies as an alternative to ascribing a physical interpretation to the potential transformations. Structural realism gets involved given its use of arguments from symmetries to a relational ontology. And the traditional distinction between symmetries of models and symmetries of laws of nature needs to be brought in to explain its relationship to the theoretical symmetries having a DES.

**In sum,** the debate about how the DES contributes to clarifying the ontology of theoretical symmetries needs to be carried out, and that is what the conference aims to do.