# Why are string theorist so indifferent to the gauge structure of gravity?

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Gravity shares many of the characteristics of Yang-Mills gauge theory. For example, the affine connection plays the similar role as the gauge potential in gauge theory, the Riemann tensor plays the same role as the field strength in gauge theory. And both theories can be well described by Fiber bundle.

I know there is a correspondence between gravity and gauge theory in string theory. But as mentioned above, can't gravity just be a gauge theory itself? The similarity is so strong that I do think gravity emerging from other possibilities is extravagant such as emerging as the requirement of the vanishing of Beta function. Actually, there are indeed some physicists do think that gravity is exactly a gauge theory of Yang-Mills type with gauge group being Poincare group, but it seems that this view is generally neglected by string theorists. Please give me some convincing reasons that this similarity should not be taken seriously. Thanks very much!

edited Apr 3, 2016

I asked this question simultaneously here and at physics stackexchange. I hope this would not be a problem.

The main point is that the full group of symmetries is the group of diffeomorphisms. One of the consequences is that there are no true local gauge invariants, there are only global (or somehow semi-local) ones.

I don't think string theorists are indifferent to the gauge structure, after all, lots of SUGRA calculations are done in the spirit of "gravity is exactly a gauge theory of Yang-Mills type with gauge group being Poincare group", and string theorists certainly care about SUGRA.

The problem is there is no straightforward way of quantizing/UV completing gravity, for example a modest kind of UV completion is perturbative renormalizability, and this fails for gravity for well known reasons. So the current popular view is that gravity must emerge as an effective field theory from something else.

You are not quite correct. Poincare group is global group and is not gauged so nobody really thinks of Poincare group as a gauge group. Additionally in GR the group that leaves the action invariant is the one which leaves $\sqrt{g}R$ invariant. In SUGRA R-symmetries are gauged.

As for the question, I think that it depends on what you call gauge theory. If you define it in terms of a connection on a principal G-bundle then it is not. But, taking GR or Einstein part of SUGRA to vielbein formalism will yield many similarities to usual Yang-Mills theories. In the end of the day, you can naively say that GR is square root of Yang-Mills, since at least on the level of on-shell amplitudes the graviton one can be written as the square of a gluon one (I do not know details on it though).

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