Does two dimensional life exist? What would the physics of a 2D universe look like? Cosmologist Dr. James Scargill recently examined and released in a preprint on June 2019.
Dr. Scargill's website: http://www.jamesscargill.com/
Dr. Scargill's paper: https://arxiv.org/abs/1906.05336

We have 3D + 1D of time. Why aren’t there 4 dimensions or 2 dimensions? Can life exist in the 4th dimension? Is there something special about three dimensions that makes life possible? This is the question that But maybe our thoughts are based on an anthropic bias. Lets look at the case for 4D. Orbits would be unstable against small perturbations from gravity coming from the extra dimensions, and so planets could not orbit stars, and solar systems could not exist in 4D. No orbits means no solar system, and presumably no life. Also gravity waves using LIGO suggest that there are no higher large dimensions. So if higher dimensions exist, they exist on very small scales – on the scale of Planck lengths where the tiny strings of string theory can vibrate. But why can’t life exist on these small scales? Because scales are so small that not even an atom could fit on these scales.

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What about 2 dimensions? Most scientists had believed that two dimensional life was impossible, but in a paper published in June, 2019, Dr. James Scargill examined the scientific possibility of two dimensional creatures. There have been two main arguments against the possibility of life in two dimensions. First because gravity according to general relativity requires 3 spatial and 1 time dimension. In other words, there would not be enough degrees of freedom for space-time to curve.

And second, scientists have believed that the neural networks for complex brains, which require hundreds of connections per neuron, could not form enough connections in two dimensions because the number of connections would be physically limited compared to three dimensions.

In two dimensions, if only the equations of general relativity were applied, gravity would exist only inside mass/energy. And so outside a star, where there is no matter, space-time must be flat, meaning no gravity, and hence there are no orbits. Why does this happen? Because there is not enough freedom in how space-time can curve, and it is instead completely determined by the matter/energy content of the spacetime.

This seems to present the same problem that we had for 4 or more large spatial dimensions. But nothing forces gravitational theory to be only defined by general relativity. A two dimensional world could have a simple scalar field. Dr. Scargill presents an exhaustive theory of scalar gravity that could be accommodated in two dimensions, which is represented by this graphic. It would allow stable orbits around point sources.

Would the other three fundamental forces from the standard model exist? – the strong nuclear force, the weak nuclear force, and electromagnetism? Yes. Two dimensions would not be a limiting factor since 2 dimensions provides enough degrees of freedom for the respective equations to work.

2D atoms could exist, because the strong nuclear force binding protons and neutrons together in the nucleus would be present, electrons could orbit around the nucleus since electromagnetism should also exist. In addition, the Higgs field would exist with no problem in principle. The Higgs Field and the weak nuclear force are probably not required for life to exist anyway.

What about the complexity of life because of the limitations on the number of neuronal connections that you could have?
Dr. Scargill shows in a series of planar 2D graphs, connections could be made with nodes, such that they exhibit complex communications networks. They would not have the complexity of three dimensional brains but they could come close if the brains were much larger.

So what would be some of the limitations for two dimensional life forms? Organic chemistry depends on the 3D shapes of molecules as well as their composition, so this kind of chemistry would be a limitation in 2D. However, this does not preclude some other form of equally effective organic chemistry to rule the 2D universe. Scientists such as A K Dewdney studies suggest that 2D chemistry could be quite sophisticated.

For any organism to exist and thrive, it has to be able to consume and process energy. It could not have a digestive tract going one way, completely through its body like you and I, because this would cut the organism in half. But, it could consume food in the same orifice that it releases its waste.

Heat dissipation would be an issue because the relative surface area for 2D creatures would be much smaller than for 3D creatures. So, the creature in order to increase its surface area for heat dissipation would have multiple folds like a radiator to dissipate more heat away from its body.