Physics 234B: String Theory II

Quantum Gravity and Unifications

Spring 2015

Basic Info

Time: lectures: Tue and Thu, 12:40-2pm.
discussions: TBD.

Place: 402 Le Conte Hall

Instructor: Petr Hořava (email:
Office: 401 Le Conte Hall.

This year, our focus in the 234B course will be on gravity -- both classical and quantum, how it emerges from string and superstring theory, whether it can have an independent life outside of strings, how it enters into various dualities and unifications across different areas of physics (from supersymmetric unifications with the Standard Model of particle physics, to unifications with non-gravitational physics via the AdS/CFT correspondence and other dualities, to nonrelativistic Lifshitz gravity and its relation to the Causal Dynamical Triangulations approach to quantum gravity, to applications in condensed matter physics). We will also discuss some of the many fundamental open puzzles of gravity.

A slightly more detailed plan for this course is as follows:

1. Survey of (semi)classical gravity.
This Chapter will serve a two-fold purpose: First, it is an introduction into the subject, making sure that we all start on the same page. Secondly, it will give a first glimpse of what are some of the fundamental puzzling features of gravity, from the perspective of many-body physics and quantum field theory, especially from the viewpoint of the renormalization group.

2. Superstring theory as quantum theory of gravity.
Strings and M-theory give us a beautiful, self-consistent and very rich arena for understanding how gravity can be combined with quantum mechanics. We will discuss first the question "Why Strings?", and will see several independent reasons why strings are special among objects of all possible dimensions. Then we will focus on the spacetime supergravity description, and discuss various string-string dualities and unifications.

3. AdS/CFT correspondence and holography.
AdS/CFT correspondence is perhaps the most successful byproduct of string theory. It is a duality, relating a seemingly non-gravitational quantum field theory on one hand, to a system with gravity (such as string theory) on the other. It therefore represents another "unification", of gravity with field theories both relativistic (of interest to particle physicists) and nonrelativistic (of interest to condensed matter and statistical physics). It also represents a constructive example of the (still rather mysterious) "holographic behavior" of quantum gravity, predicted by robust arguments based on the thermodynamic properties of black holes.

4. Effective field theory of gravity.
We will examine relativistic gravity using the framework of low-energy effective field theory. In this picture, the cosmological constant problem arises as the most pressing of all Naturalness problems. I will review the concept of technical Naturalness. We will also discuss the Appelquist-Carazzone decoupling theorem (and whether it should apply to gravity), and take a look at various previous attempts how to solve the cosmological constant problem. Also to be included: the Weinberg-Witten theorem; and at least a brief discussion of the recent "amplitudes" approach, including the color-kinematics duality.

5. Keldysh-Schwinger formalism, QFT out of equilibrium.
One of the best guarded secrets in theoretical physics: Relativistic QFT, as it is usually taught in our high-energy theory courses, is only a fragment of the whole story! It is a simplification of the whole thing, resulting from the assumption that the system has a stable, static and eternal vacuum. However, this assumption -- while OK for scattering particles at colliders -- seems rather dubious for gravity, especially when we take into account that we live in an evolving cosmological universe. The whole story of QFT without the simplifying assumptions about the vacuum is known for historical reasons as the "Keldysh-Schwinger formalism" -- I will review its basics, and take a look at how it is slowly making its way into quantum gravity.

6. Nonrelativistic gravity (often now called "Hořava-Lifshitz gravity"), causal dynamical triangulations.
This is a rather novel approach to making sense of gravity in a quantum theory, and it has attracted a lot of attention. The basic idea is to take QFT and the renormalization group seriously, but Lorentz invariance not so seriously. I will review the basics, including some applications to nonrelativistic AdS/CFT correspondence, and the comparison to the Monte Carlo lattice approach to quantum gravity known as Causal Dynamical Triangulations.

7. Effective field theory of inflation.
Methods of effective field theory have now been successfully applied to inflationary cosmology, a setting in which gravity and its quantum features are at the forefront. We will review the basics of this approach, and point out its connections to some of the previous Chapters discussed in this course.

Clearly, this is a rather ambitious and long list, which means that we will only be spending about two weeks on each of the 7 Chapters. At that pace, I expect that we will have covered Chapters 1 through 4 around Spring break, leaving Chapters 5 through 7 for after the break.

Miscellaneous References

Here I will be posting various comments, references and extra reading material options, on a weekly basis as we go through the material.

Week 1. Before we can quantize gravity we need to understand its basics classically. You can review classical General Relativity by leafing through Sean Carroll's book

S.M. Carroll, Spacetime and Geometry. An Introduction to General Relativity, Addison Wesley, 2004.

This book is now a classic, and your first reference if you need to refresh your memory on anything in classical GR.

Week 2. I mentioned in lecture that relativistic gravity with the general R-squared Lagrangian in 3+1 dimensions is formally asymptotically free, but when interpreted in Minkowski signature it suffers (at least on first inspection) from the presence of propagating ghosts and hence apparent violations of unitarity. Per audience request, here is a reference that discusses renormalization of the higher-derivative gravity and contains further useful references:
R. Percacci, A Short Introduction to Asymptotic Safety, arXiv:1110.6389.


On the gravity side, basics of General Relativity at the level of 231 are required. On the quantum side, basics of QFT at the level of 232A would be a good start, and will effectively be required.

On the other hand, basics of Yang-Mills gauge theories (either 233A or 232B) would also be useful, but will not be strictly required for students who wish to sign up for this course. Same with the basics of String Theory -- it would be useful and nice to have seen strings (at the level of 234A), but it will not be formally required in order to take this course. If you are interested in this course and have questions about having all the prerequisites, feel free to talk to me (in person or via email); I will try to be flexible, so that we can accommodate as many students in this course as possible, even those who come from various diverse backgrounds such as particle phenomenology, cosmology, condensed matter, or pure math.

Homeworks and Reading Assignments

There will be no homework sets for this course. Instead, there will be a list of reading assignments, where each student gets to choose one from the list of many important gravity-related research papers. Then, in the second half of the semester, the students will present their summary of the ideas and results of their chosen paper during our Discussion Sessions. The final grade will be based on this presentation. There will be no final exam.