Researchers demonstrate constraints on symmetries from holography

Researchers demonstrate constraints on symmetries from holography
The figure shows the essence of the researchers’ argument against global symmetries. They assume that a global symmetry exists and also that the object in the center of the diagram is charged under the symmetry, and then show that this would require the object to be in the shaded grey regions, which it isn't; this is proof by contradiction! Credit: Harlow & Ooguri.

A pair of researchers, one at the Massachusetts Institute of Technology (MIT) and another at California Institute of Technology (Caltech) and the University of Tokyo, have recently investigated a set of old conjectures about symmetries in quantum gravity. The specific conjectures of focus: (1) Quantum gravity does not allow for global symmetries; (2) For gauge symmetry, all possible charges must be realized; (3) Internal gauge groups must be compact. Their paper, published in Physical Review Letters, shows that these old assumptions hold within the anti-de Sitter/conformal field theory (AdS-CFT) correspondence.

"Historically, the concept of symmetry has played important roles in physics, both in identifying and formulating fundamental laws of nature, and in using these laws to understand and predict natural phenomena such as dynamics and phases of matters," Hirosi Ooguri, one of the researchers who carried out the study, told Phys.org. "However, there has been theoretical evidence to suggest that, once we combine and (the two fundamental ideas in modern physics), all global symmetries are gone."

In physics, symmetries can be of two kinds: gauge and global. For several decades, researchers have proposed the idea that global symmetries should not be possible in , as the unified theory of gravity and quantum mechanics would not allow for any symmetry. This is a profound claim with important consequences. For instance, it predicts that a proton would not be stable against decaying into other particles.

"The standard model of particle physics has both kinds of symmetries, so we are predicting that the global ones must only be approximate," Daniel Harlow, the other researcher involved in the study, told Phys.org. "So far, this idea has had some circumstantial support, but there was no convincing argument. In our paper, we gave what we think is a rather convincing argument in the special case of the AdS/CFT correspondence. This correspondence gives our best-understood theories of quantum gravity, and we were able to show that it does not allow global symmetries."

Prior to Ooguri and Harlow's paper, other researchers made arguments supporting the claim that quantum gravity (the unification of quantum mechanics and gravity) cannot have any symmetry. Nonetheless, these arguments often presented logical gaps or loopholes, for instance failing to address some important cases (e.g. discrete symmetry).

"Our new paper provides a rigorous proof of this claim in the context of the AdS/CFT correspondence, where quantum gravity is defined in a mathematically precise way, and we have done so in the most general way, excluding all possible global symmetries from quantum gravity," Ooguri said.

The proof presented by Ooguri and Harlow is based on two important ideas: the holographic principle of quantum gravity and quantum error correcting codes. The holographic principle was first introduced by Gerard 't Hooft and Leonard Susskind in the early '90s, yet it has since been widely built upon. One of its most crucial developments was the discovery of the AdS/CFT correspondence by Juan Maldacena in 1997.

Ooguri and Harlow wished to prove a mathematical theorem on quantum gravity, so they required a precise definition of the holographic principle. They decided to adopt the AdS/CFT correspondence, as this was the only way they felt they could achieve their goal.

"Our basic tools are quantum error correction, the AdS/CFT correspondence, and quantum field theory," Harlow said. "Probably the most important point to convey here is that although AdS/CFT is a beautiful theory of quantum gravity, it is not the theory of quantum gravity in our world. It is a toy model of the type that physicists like to study (such as the famous spherical cow). We believe, however, that lessons we learn in this toy model should carry over to our world provided that we are careful."

A few years ago, a different research group that also included Harlow showed that holography works in quantum gravity in a similar way to how quantum error correction works in quantum computing. In the AdS/CFT correspondence, spacetime geometry in the anti-de Sitter Space emerges from quantum entanglement in the conformal field theory. Harlow and his colleagues showed that the emergent geometric data is, in fact, quantum error correcting codes, from a CFT standpoint.

The insight from this previous research was essential to prove the theorem in the researchers' recent study. In their new study, Ooguri and Harlow found that the way quantum error correction works is not compatible with any symmetry. Thus, once quantum mechanics and gravity are merged, no symmetry is exact.

"It has generally been believed that symmetry is a fundamental concept in nature," Ooguri said. "Many physicists believe that there must be a beautiful set of laws in nature, and that one way to quantify beauty is by symmetry. Some of the symmetry may be hidden in our world (or 'spontaneously broken," in physics terms), but they may manifest themselves if we look at nature at a more fundamental level. We showed that the belief expressed in the above is wrong. The laws of nature at the most fundamental level, where quantum mechanics and gravity is unified, have no global symmetry."

The study carried out by Ooguri and Harlow brings key insight to the physics field, ruling out the possibility of global symmetries in a wide class of quantum gravity theories. Their findings have implications for numerous areas of study, for instance predicting the instability of protons.

"Our findings predict that the proton should not be stable," Harlow said. "It isn't obvious, but it also predicts the existence of magnetic monopoles: isolated objects which carry magnetic charge. So far, we have never seen such an object, but people are still searching for them. Unfortunately, our results are not strong enough to say how many monopoles should exist, where they should be, or how long we have to wait to see a proton decay."

In their future work, Harlow and Ooguri would like to quantify how symmetry is broken. So far, they have merely proved that quantum gravity cannot have any symmetry without clarifying how it is taken apart. For instance, their findings suggest that the proton should decay, yet they do not clarify how it decays or how long it can live for before it does. These are very important questions, which the researchers hope to address in their future research.

"The Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, of which I am the director, is involved in the Hyper-Kamiokande project to be built in the Kamioka zinc mine in the central mountain area in Japan," Ooguri added. "One of the aims of the project is to see whether the proton decays and to do this experimenters will build a large water tank in the mine. According to our theorem, the protons should decay. But, we cannot tell experimenters how big the water tanks should be for them to be able to see the protons decay within a reasonable period of time. This is one example of why quantifying how symmetry is broken would be crucial. Daniel and I have some idea on how to quantify the way is broken and we are now continuing our investigation in this direction."


Explore further

How spacetime is built by quantum entanglement

More information: Daniel Harlow et al. Constraints on Symmetries from Holography, Physical Review Letters (2019). DOI: 10.1103/PhysRevLett.122.191601

Daniel Harlow, Hirosi Ooguri. Symmetries in quantum field theory and quantum gravity. arXiv:1810.05338 [hep-th]. arxiv.org/abs/1810.05338

G. 't Hooft. Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026. arxiv.org/abs/gr-qc/9310026

L. Susskind. The world as a hologram. arXiv:hep-th/9409089. arxiv.org/abs/hep-th/9409089

Juan M. Maldacena. The large N limit of superconformal field theories and supergravity. arXiv:hep-th/9711200. arxiv.org/abs/hep-th/9711200

Journal information: Physical Review Letters

© 2019 Science X Network

Citation: Researchers demonstrate constraints on symmetries from holography (2019, May 28) retrieved 24 June 2019 from https://phys.org/news/2019-05-constraints-symmetries-holography.html
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May 28, 2019
At first glance these results would seem to give a boost to Penrose's CC Cosmology. If I'm not mistaken his conformal mapping requires all massive particles to be converted to photons. Well, if the absence of global symmetry means that Protons decay in some finite time, that's a step in the right direction.

May 28, 2019
At first glance these results would seem to give a boost to Penrose's CC Cosmology. If I'm not mistaken his conformal mapping requires all massive particles to be converted to photons. Well, if the absence of global symmetry means that Protons decay in some finite time, that's a step in the right direction.
Yes, and the arbitrarily long temporal scales of CCC easily dwarf any reasonable half-life of the proton, plus the fact that the main mass––>energy engines would be Hawking-radiating black holes. After a googolplex of years, nothing would remain but a heat-death EM and neutrino soup, having no means of self-mensuration. In such a 'universe', it would be meaningless to speak of long or short, temporally or spacialy. It would continue in its geriatric exponential expansion into a nascent Guthian inflation seamlessly.

May 28, 2019
CCC vs free parameterization does not matter. An ontic duality, of the one and the many or some effective theory of gravity causing a state reduction, is merely two isotropic perspectives on unitarity. Any super symmetric account exceeds, or is on unitarity, (not necessarily with evolution), to extract a pragmatic form to transact. The far side of flop is not considered serene. Where as the Penrose formulation has gravity perform a state reduction, reserving parity to not distinguish chirality. It saves relativity, and can allow an auxiliry with general relativity, however, does it matter? Especially if the extension of relativity for completeness is more useful. Ontic divergence, may not be known, but the map is better than the territoty with its free degrees. The unknown is a choice at that point, rather than deloading to a lack of clairty. CSWAP or CNOT, these gates make no difference, but from one known we can discern and invent the unknown. Separability or the storm ever further.

May 28, 2019
This from the researchers...
"Our findings predict that the proton should not be stable," Harlow said. "It isn't obvious, but IT ALSO PREDICTS THE EXISTENCE OF MAGNETIC MONOPOLES: isolated objects which carry magnetic charge. So far, we have never seen such an object, but people are still searching for them. Unfortunately, our results are not strong enough to say how many monopoles should exist, where they should be, or how long we have to wait to see a proton decay."
...should ring alarm bells! This is all mathematical gymnastics, juggling things that can have no physical existence in reality. As they themselves admit when they oh-so-by-the-way-casually point out that their theorem/exercise is based in the shaky terms/assumptions/constructs of what they also casually acknowledge are speculative 'toy model' conjectures (and no more than that).

In re 'global' symmetry: it has ALWAYS been LOGICALLY OBVIOUS that NO such thing can obtain; else we would not BE here. :)

May 28, 2019
Global symmetry can occur, but only once. Or rather it is not possible to tell if future space-time decompactification, of the bits flipping, is also a reset. A point. Or a seed from positive pressure and negative pressure, near missing. Or an orbifold of cyclic features projected.... Welcome to the debatably vanishing or collectively exhaustive.

May 28, 2019
Global symmetry can occur, but only once. Or rather it is not possible to tell if future space-time decompactification, of the bits flipping, is also a reset. A point. Or a seed from positive pressure and negative pressure, near missing. Or an orbifold of cyclic features projected.... Welcome to the debatably vanishing or collectively exhaustive.
"When I meet someone on a professional basis, I want them to shave their arms. While at a conference a few weeks back, I spent an interesting evening with a grain of salt. I wouldn't dare take them seriously! This brings me back to the brash people who dare others to do so or not. I love a good flame argument, probably more than anyone..." &etc. --Mark V. Shaney

May 28, 2019
..should ring alarm bells! This is all mathematical gymnastics, juggling things that can have no physical existence in reality.
No alarm-bells. Magnetic monopoles figure in a number of reasonable theories, and even have significant explanatory power. Cf
phys.org/news/2016-09-theories-magnetic-monopoles.html
The main objection is that The Standard Model does not predict/require them. Non-requirement has become a proxy, in modern physics formalism, for non-existent; this is parsimony.

May 29, 2019
@danR.
..should ring alarm bells! This is all mathematical gymnastics, juggling things that can have no physical existence in reality.
No alarm-bells. Magnetic monopoles figure in a number of reasonable theories, and even have significant explanatory power. Cf
phys.org/news/2016-09-theories-magnetic-monopoles.html
The main objection is that The Standard Model does not predict/require them. Non-requirement has become a proxy, in modern physics formalism, for non-existent; this is parsimony.
Actually, reasonable physicists view predictions of Magnetic Monopoles as a 'prima facie' indicator that a hypothesis is NOT 'reasonable'; ie, most likely NOT CONCORDANT with physical reality. Other such indicators being: predictions of Time Travel and Anti Gravity (and also Perpetual Motion other than that of the overall totality of physical entities/processes constituting/manifesting the unceasing cycling/recycling energy-space of infinite/eternal Universe itself). :)

Jun 07, 2019
Looks like they're indirectly suggesting only Einstein's gravity can conserve the proton forever. You know general relativity fans are going to eat it up and then try to drown everyone in it. I don't even know what temperature is best for this bath.

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