Low Energy? Think Positive!

Scott Melville, winner of the Best Student Talk Prize at BritGrav, which was sponsored by CQG, discusses the research that he’s doing on quantum gravity at Imperial College London.

Image courtesy of Steve Cross

Scott Melville, speaking at Bright Club on 28th April 2018. Image courtesy of Steve Cross

The present state of quantum gravity is rather unsatisfying. While perturbation theory works well at low energies, at high energies quantum gravity becomes incalculable, and leaves us hungry for answers. As we approach the Planck scale, perturbations become strongly coupled and we quickly lose perturbative control of our theory. A UV complete theory of gravity, which remains unitary and sensible to arbitrarily high energies, is hard to cook up.

We need new physics, to swallow these Planck-sized problems. This new physics shouldn’t be too heavy, or too light; not too strongly coupled, or too perturbative. We don’t yet know exactly what it should be, but it needs to hit a sweet spot. My research develops tools, called positivity bounds, which can help us better understand how low energy observables are connected to this unknown new physics.

One thing is for certain: quantum gravity is hard – and working on it sure builds up an appetite. When I’m not worrying about the fundamental nature of the Universe: I’m in the kitchen. While I may not be the best chef in the world, I make up for an abysmal lack of skill with a towering surplus of enthusiasm. You can flip anything in a pan, if you flip hard enough.

When it comes to deciding what to have for dinner, I take things very seriously: it can’t be too salty, or too sweet; not too spicy, or too bland.

If I’m feeling ambitious, I’ll try to tackle the problem in one blinding flash of culinary inspiration – by closing my eyes and plucking my perfect dish, fully formed, from the ether. But this leads to nothing but disappointment. As a graduate student, my kitchen cupboards are sparse. More often than not, my lofty imagined dish is just not consistent with my lowly actual ingredients. Instead, I often have more success working from the bottom-up – by starting from the few ingredients that I have, and asking more modest questions such as, `could these things ever make a meal?’

I approach quantum gravity like I approach cooking.

The image is adapted from the Public Domain image: https://commons.wikimedia.org/wiki/File:Moon_over_Miami_cooking.JPG

The leading non-trivial corrections to Einstein’s General Relativity (which cannot be removed by field redefinitions or integration by parts in four dimensions) are both constrained by positivity bounds [see, for instance, PhysRevD.93.064076].

Given the very few data points we have, it’s very difficult to decide on a full UV completion all in one go. Some popular recipes for particular UV quantum gravities do exist, and while their study is certainly fruitful, I wish to remain agnostic. Instead, I work with effective field theory (EFT) – low energy descriptions which capture the long-scale world. Then I ask questions like: `can this EFT ever be embedded into a delicious UV complete theory, which works over very small distances?’

If a UV completion has certain flavours, then it must contain certain ingredients in the IR. In particular, if a theory is to be unitary and causal at high energies (thanks to new heavy degrees of freedom à la Wilsonian RG flow), then at low energies the corresponding EFT operators must satisfy certain relations. These are known as positivity bounds.

This connection between certain properties of the unknown UV and the low energy EFT observables is important for two crucial reasons.

Firstly, there are many different EFTs which are consistent with our limited gravity observations, and without being able to distinguish them further we cannot make unique or reliable predictions. Demanding that a sensible UV completion exists can provide constraining power for our underdetermined field theories.

Secondly, if one gives up any connection between the unknown UV physics and the low energy EFT observables, then the only way to learn about quantum gravity would be to perform genuinely Planck scale experiments (!). Instead, we should try to use our low energy observables to identify properties of the UV, such as its symmetries or analyticity properties.

So as we gain access to increasingly numerous and more precise data from gravity and cosmology, exploiting these connections between large and small scales has never been more important. Particularly promising is the effect that positivity bounds have on constraining features of gravitational waves. With the advent of gravitational wave and multi-messenger astronomy, measuring these effective corrections to gravity seems tantalizing close. In the days and years to come, positivity bounds will continue to improve the predictivity, and our understanding, of quantum gravity.

If you haven’t the time to digest all that, then the takeaway messages are simply:

  • Effective field theories are only predictive once you supply enough data (to fix all of the couplings). For gravity and cosmology, there is often not enough data and so accurate predictions require an additional means of fixing coefficients.
  • While the exact nature of the UV completion is unknown, certain properties (such as unitarity and causality) seem like safe assumptions. In order for these properties to be upheld in the UV, the EFT couplings must satisfy certain positivity bounds.
  • Exploiting this connection in reverse, if one measures the couplings in a low energy EFT, whether they satisfy these bounds provides non-trivial information about the deep UV!

So if quantum gravity is eating away at you, and this blog post has whet your appetite for a solution, you can read more about positivity bounds in our series of recent papers:

“Positivity Bounds for Scalar Theories”, C. De Rham, S. Melville, A. Tolley and S.-Y. Zhou, https://arxiv.org/abs/1702.06134PhysRevD.96.081702

“Improved Positivity Bounds and Massive Gravity”, C. De Rham, S. Melville and A. Tolley, https://arxiv.org/abs/1710.09611 : JHEP04(2018)083

“Positivity Bounds for Massive Spin-1 and Spin-2 Fields”, C. De Rham, A. Tolley, S. Melville and S.-Y. Zhou, https://arxiv.org/abs/1804.10624

About the author: Scott Melville currently holds the President’s PhD Scholarship at Imperial College London, working with Claudia de Rham and the Theoretical Physics Group. Scott recently received the Student Talk Award from CQG at BritGrav 2018 in Portsmouth, for his presentation of `Positivity Constraints for Gravity and Cosmology’. From October 2018, Scott will take up a Research Fellowship at Emmanuel College, Cambridge.

Personal Website: www.scottamelville.com/

Group Website: http://www.imperial.ac.uk/theoretical-physics

This work is licensed under a Creative Commons Attribution 3.0 Unported License.