Quanta: how fractons can help realize quantum computing, break the Standard Model and realize quantum gravity?

[notFritzArgelander]

intuitively it seems that fractons have just the properties needed to make spacetime emergent from a revised Standard Model and Quantum Field Theory. this is an important new line of research.

https://www.quantamagazine.org/fractons ... C98Xf5FLnc

[GCoyote]

Got the pdf version. Hope to get to it this evening.

[notFritzArgelander]

Got the pdf version. Hope to get to it this evening.

You mean this? https://arxiv.org/abs/2003.10466

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

[notFritzArgelander]

Of the various approaches to quantum gravity I think that the fracton idea might be most useful in causal set approaches. I'm not saying that neither loop quantum gravity nor string theory approaches couldn't benefit too, just that the fracton concept seems to my mind to be more amenable to the structure of causal sets.

[GCoyote]

Got the pdf version. Hope to get to it this evening.

You mean this? https://arxiv.org/abs/2003.10466

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

No, Quanta has a direct to pdf option on the page. I like that they don't make you jump through hoops like some webzines to get a copy for later reading or for reference.

[notFritzArgelander]

Got the pdf version. Hope to get to it this evening.

You mean this? https://arxiv.org/abs/2003.10466

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

Well I've had a first cut at reading this preprint and I have to say it's given me a migraine. Some of the prose seems quite promising, some seems disappointing. However most of the mathematical details are escaping me at the moment. I think that my ability to read QFT papers at this level is not what it used to be. I'll take 2 aspirin and try again tomorrow morning.

[notFritzArgelander]

There are a few points in the preprint that I mentioned above as hopeful and discouraging.....

https://arxiv.org/pdf/2003.10466.pdf

The spectrum includes massive particles (fractons) of restricted mobility. Some particles are completely immobile, or can move only along a line, or along a plane. In our treatment of these models we will focus on the low-energy theory. It does not include such dynamical excitations. However, the effect of these massive particles is captures by defects, whose locations are restricted. These defects can be thought of as deformations of the Hamiltonian along lines (or strips) stretched along the time directions.

This suggests to me a model in which fractons capture the function of a background space time while the particles of the Standard Model are charged defects that have timelike propagation among the fractons. Also

These systems exhibit exotic global symmetries. Some of these global symmetries are known as subsystem symmetries.2 These are symmetries whose charges act only on a subspace of the total space. Unlike the generalized global symmetries of [9], here the value of the charge varies from subspace to subspace [10]. If the global symmetry group is compact such as U(1) or ZN, this means that the charge operator can be discontinuous as a function of the position.

On the discouraging side of things is the remark:

Not only will these quantum fields theories not be Lorentz invariant, they will also not be rotational invariant. In this paper we will focus on 2 + 1-dimensional systems and we will not preserve the full SO(2) rotation symmetry, but only its subgroup of 90 degree rotations, Z4.3 (We will denote its irreducible, one-dimensional representations 1n with n = 0,±1,2 labeling the spin.) We will not impose parity or time reversalsymmetries, although many of our models are invariant under them. In addition, we have the continuous translation symmetries both in space and time.

It can be expected (or more cautiously hoped) that in the continuum limit all the appropriate symmetries are recovered.

Perhaps the most significant new element is that we will consider discontinuous fields.4 The underlying spacetime will be continuous, but we will allow discontinuous field configurations. Starting at short distances with a lattice, all the fields are discontinuous there. In standard systems, the fields in the low-energy description are continuous. Here, they will be more continuous than at short distances but some discontinuities will remain.

The allowance of discontinuous field in the continuum limit is interesting..... That would localize particle like behavior.

I'm intrigued. I want to read more. The question is how high my pain threshold might be?

[GCoyote]

Maybe we should start a go fund me page to provide you with suitable pain relief. It's the least we can do.
:veryconfused:

[notFritzArgelander]

Maybe we should start a go fund me page to provide you with suitable pain relief. It's the least we can do.
:veryconfused:

It’s a problem that my QFT skills are rusty. The remedy might take more time than I have.