# What would it mean if symmetries are not fundamental at all?

In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:

From more theoretical points of view, string theory appears to allow no exact global symmetries, and in any theory of quantum gravity virtual black holes might be expected to violate all global symmetries

Moreover, as we have already discussed in §2, local (gauge) symmetries have been demoted as well, with the discovery of many and varied systems in which they emerge essentially from nowhere. It seems that local symmetry is common, not because it is a basic principle, but because when it does emerge it is rather robust: small perturbations generally do not destroy it. Indeed, it has long been realized that local symmetry it is ‘not really a symmetry,’ in that it acts trivially on all physical states. The latest nail in this coffin is gauge/gravity duality, in which general coordinate invariance emerges as well.

This leaves us in the rather disturbing position that no symmetry, global or local, should be fundamental (and we might include here even Poincaré invariance and supersymmetry). Susskind has made a distinction between the mathematics needed to write down the equations describing nature, and the mathematics needed to solve those equations. Perhaps symmetry belongs only to the later.

I have a few questions about these claims:

1. Polchinski mostly worked in string theory and ideas related to it. Is it there any model in string theory or any related theory which proposes that symmetries may not be fundamental at all?

2. If no symmetries are fundamental, would this mean that there are no fundamental laws of physics? Would this mean that all symmetries (and all laws associated with them) would be rather emergent?

• Can you clarify "If no symmetries are fundamental, would this mean that there are no fundamental laws of physics?" Exact global symmetries are thought to be incompatible with any theory of quantum gravity. This is the theme of the paper Symmetries in Quantum Field Theory and Quantum Gravity, which reviews some traditional arguments and presents a more robust argument using one example of a quantum gravity theory (AdS/CFT). Oct 21, 2020 at 13:43

1) There are examples from string theory, supersymmetric gauge theories and matrix models that indicate that symmetries may not be fundamental

Examples:

1. Sometimes a theory with (local/global) a gauge symmetry is dual to a theory with a different gauge symmetry, or no gauge symmetry at all. An interesting example is Maxwell theory in three dimensions, this is a U(1) gauge symmetry with an electric-magnetic dual description in terms of a free massless scalar with no local gauge symmetry. See https://arxiv.org/abs/hep-th/9506077 for this example, and https://arxiv.org/abs/hep-th/9509066 for more elaborated examples.

2. Emergent general covariance: Matrix models in triangulated random surfaces (see https://arxiv.org/abs/hep-th/9304011) does not have two dimensional Poincaré or conformal symmetry at finite $$N$$. Its only in the large-$$N$$ limit that those notions emerge.

2) The possibility that gauge symmetries could not be fundamental does not rule out, in principle, the viewpoint that more general symmetries could be "fundamental"; string theory dualities are candidates, we don't have examples in in which they emerge or they could be violated.

It is perfectly possible that humans can develop laws of physics without symmetries as inputs.

• thank you for your helpful answer. I would like to ask you a few more questions about it: Even though there is still the possibility that more general symmetries would indicate which laws are really fundamental, are there any string theory model or any author working on string theory that propose that there are actually no fundamental symmetries or laws whatsoever and that they are all emergent (or at least consider that possibility)? Would the articles that you have posted be examples of that? @RamiroHum-Sah Oct 27, 2020 at 18:55
• @vengaq Sorry, as far as I can tell, nobody has written or considered a concrete scenario where all the symmetries of the system as emergent. But of course, I could be wrong. It's worth to mention that the papers I've shared and similar ones mostly discuss gauge symmetries not the status of more general symmetries. Oct 27, 2020 at 21:29