Physics 234B -- String Theory II

Spring 2020

Link to the list of Reading Assignments
Shortcut to Miscellaneous References & Reading Suggestions

Basic Info

Instructor: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte Hall.
Office hours: Originally scheduled for Tue and Thu, 2:30-3:30pm. Now I am available for Zoom meetings by email appointment.

In the past several decades, string theory has entered into the theoretical mainstream of physics, and it has become an indispensable tool in the toolbox of modern theoretical physicists (and even mathematicians), because it has stimulated far-reaching conceptual advances not only in quantum field theory and quantum gravity, but increasingly across many other fields, including particle phenomenology, observational cosmology and -- with the advent of holography -- also in condensed matter physics and quantum information. As a framework that unifies quantum mechanics with gravity, geometry and general relativity, string theory is providing consistent conceptual answers to the puzzles of quantum gravity and serves as a spin-off machine, producing novel ideas in model building beyond the Standard Model, for inflationary cosmology, and via gauge-gravity dualities a novel technique for solving strongly-coupled and strongly-correlated systems using gravity duals, but also gives guidance to mathematicians how to extend geometry beyond the classical domain. In this course, I will survey this landscape of uses of string theory in diverse areas of physics (and some math), attempting to make the subject accessible not only to future string theorists but to all theorists interested in this fascinating subject.

Having learned the basic ingredients of the "string-theory alphabet" in an introductory course String Theory I, in this semester we will first review the basics of strings, superstrings of M-theory to make sure we are all on the same page, and then we will focus on several exciting advanced topics in string theory, in which the various ingredients come together (and where intriguing open challenges remain). The topics planned to be covered in our 234B include:

Part 0. Preamble: A concise summary of the basics of string theory.

Part I. String-string and M-theory dualities. Perturbative and non-perturbative dualities. Physics of D-branes. Black holes, black branes, entropy. Compactifications and string geometry, topological strings.

Part II. Holography: AdS/CFT correspondence and other holographic dualities. Phenomenological approach to AdS/CFT without string theory; derivation from D-branes and string theory; holography for nonrelativistic systems; applications to condensed matter and "AdS/CMT" correspondence.

Part III. Inflationary cosmology. Effective field theory approach to inflation, without strings; inflation and string theory; open questions in string cosmology.

Part IV. Open puzzles in quantum gravity and string theory. Puzzles of technical naturalness in Nature; cosmological constant problem. Nonequilibrium physics and string theory. Schwinger-Keldysh formalism for particles, strings and cosmology.

Some interesting textbooks that we may use (to varying degree) are:

K. Becker, M. Becker and J.H. Schwarz, String Theory and M-Theory. A Modern Introduction (Cambridge University Press, 2006).
[I use this book whenever I teach String Theory I, and it will be our go-to for the basic ingredients of the theory in the first parts of this semester.]

E. Kiritsis, String Theory in a Nutshell (Princeton University Press, 2007).
[Another good one-volume survey of the modern aspects of string theory.]

M. Ammon and J. Erdmenger, Gauge/Gravity Duality. Foundations and Applications (Cambridge University Press, 2015).
[A recent survey of the basics of AdS/CFT correspondence, a good reference text for AdS/CFT basics.]

D. Baumann and L. McAllister, Inflation and String Theory (Cambridge University Press, 2015).
[This will be our go-to text for our critical survey of inflation.]

J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, 2015).
[An entertaining introduction into modern applications of string theory, holography and AdS/CFT correspondence to condensed matter.]

Prerequisites

Grading, Homeworks, Reading Assignments

There will be no homework sets for this course. The bulk of the material will be presented in the lectures, and after each lecture a recommended reading material will be posted on this webpage for those interested in something extra beyond the lectures. Instead of homeworks, there will be a list of reading assignments (see the update dated 3/20/20 below, for details). Each student will choose one from this list of important or otherwise interesting string-related research papers. During the second half of the semester, the students will type up a two-page summary of their understanding of the material in their reading assignment. There will be no in-person or on-line presentations, instead the 2-page summaries will be emailed to me, and I will distribute them by email to our student group. The final grade will be based on completing this assignment. There will be no final exam.

Miscellaneous References & Reading Suggestions

Weeks 1 and 2: We begin the top-down descent from M-theory in 11 dimensions to superstrings in 10 and lower dimensions. First, we review the supergravity approach to M-theory: The structure of supergravity in 11 dimensions, the existence and features of M2- and M5-branes. The main reading resource for this is continuing to be Becker&Becker&Schwarz, (=[BBS]), just as in our previous semester. For the elements of M-theory and supergravity, see Chapter 8 of [BBS]; basics of black holes and their thermodynamics can be found in Chapter 11 of [BBS].
An intuitive argument about which singular solutions of low-energy (super)gravity should be kept (i.e., those that can be "thermalized") and which should be discarded (i.e., those that can't) goes back to an influential paper by the late Steve Gubser:
S.S. Gubser, Curvature Singularities: the Good, the Bad, and the Naked, arXiv:hep-th/0002160.
Next week, as we compare M-theory on the circle to Type IIA superstring theory, we will also be discussing the story of the D8-brane: An illustrative example of some of the subtleties involved in duality arguments, as discussed nicely in
E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos, and P.K. Townsend, Duality of Type II 7-Branes and 8-Branes, arXiv:hep-th/9601150.

Week 3: The worldsheet description of the Type IIA superstring in ten spacetime dimensions follows from the supermembrane worldvolume theory in eleven dimensions by a double dimensional reduction, as shown first in 1987 (!!) here:
M.J. Duff, P.S. Howe, T. Inami and K.S. Stelle, Superstrings in D=10 from Supermembranes in D=11, Phys. Lett. B191 (1987) 70.
Wow, in 1987! That's eight years before M-theory was proposed!
The configuration of M-theory in 11 dimensions with two boundaries of opposite chiralities breaks all of supersymmetry, but the anomaly cancellation persists. This nonsupersymmetric configuration was introduced and studied in some detail in:
M. Fabinger and P. Hořava, Casimir Effect Between World-Branes in Heterotic M-Theory, arXiv:hep-th/0002073.
An early, but really nice and exceptionally lucid introduction into supergravity in components (especially in 11 dimensions), including its 1.5 order formalism, is in:
P. van Nieuwenhuizen, Six Lectures at the Cambridge Workshop on Supergravity, in: Superspace and Supergravity (S.W. Hawking and M. Roček editors; Cambridge U.P., 1981). (Unfortunately I cannot find a pdf file anywhere online)

Weeks 4 and 5: We continued the discussion of all string-string and string/M-theory dualities in 10 and 11 dimensions. One reference that I promised to post the week earlier is Witten's original paper on the Kaluza-Klein instability to the decay to "nothing":
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B195 (1982) 481.

Week 6: We concluded the discussion of various string-string and string-M dualities, with the relevant material covered largely by Chapter 8 of [BBS]. The next major theme was the cancellation of spacetime gauge/gravitational anomalies. We developed the BRST-based understanding of anomaly analysis (a universally important topic, covered really well in Weinberg's The Quantum Theory of Fields Vol. 2, Chapter 22 (especially section 22.6), and then we applied it first to the anomaly cancellation in ten-dimensional superstrings at weak coupling and the Green-Schwarz mechanism, and then to heterotic M-theory which requires a refinement of the standard Green-Schwarz mechanism. These topics are covered in [BBS} Ch. 5.4 and the heterotic M-theory case in more detail in
P. Hořava and E. Witten, Eleven-Dimensional Supergravity on a Manifold with Boundary, arXiv:hep-th/9603142.

Week 7: Having understood the vacua of string and M-theory in 10 and 11 dimensions, we started the descent towards compactifications to lower spacetime dimensions. First we discussed toroidal compactifications with maximum number of 32 supercharges, leading to the exceptional-symmetry pattern and U-duality groups mapped out nicely in Chapter 11.6 of E. Kiritsis's String Theory in a Nutshell (1st ed). Then we discussed in detail the subject of "String/Quantum Geometry", in particular Calabi-Yau (CY) compactifications. The importance is both for physics and for math, depending on context: On the physics side, heterotic compactifications to 3+1 dimensions on a CY 3-fold follow from the requirement of N=1 supersymmetry, and chirality of matter. Beautiful connections to grand-unified GUT theories with exceptional symmetry follow, and we discussed their connection to (beyond) Standard Model physics both at weak string coupling, and at strong coupling using heterotic M-theory. On the math side, compactifying Type IIA/B on a CY 3-fold leads to moduli spaces with 8 superchages, exhibiting beautiful mathematical phenomena such as Mirror Symmetry. Much of the material is explained in Chapter 9 of [BBS], which is a useful starting point before going into more literature.

Week 8: As of Monday, March 9, the campus has officially announced that our in-person classes will be stopped due to the corona-virus precautions. There will be no lecture on Tuesday, March 10, as I prepare the transition to an on-line lecturing system. I am hopeful to resume this course via on-line lectures effective this Thursday, March 12.
In the meantime, all students are assigned the following reading homework: Please complete the reading of Chapter 9, especially the following sections -- 9.5, first half-page of 9.6, and sections 9.7 and 9.9. Our previous discussion of U-duality for 32 supercharges gives you enough understanding to read sections 9.11 and 9.12 as well.
In addition, I wish to point out at least two papers for further optional reading. For a great review paper on supersymmetric black holes in string theory with 8 supercharges, including implications of mirror symmetry, see:
M. Guica and A. Strominger, Cargese Lectures on String Theory with Eight Supercharges, arXiv:0704.3295.
For an overview of the worldsheet approach to Mirror Symmetry (where it was historically first discovered), see:
B. Greene, String Theory on Calabi-Yau Manifolds, arXiv:hep-th/9702155.
This will wrap up our discussions of string compactifications and quantum geometry. If you have questions about the material, I am available to consult by email. Starting from Thursday March 12, we will move on to the next major part of this course: holography and AdS/CFT correspondence.

Update (Wednesday March 11, 11:30am): The lectures with resume online, via Zoom. Our first Zoom lecture will be live, on Thursday March 12, at the usual time of 12:40pm. I will send the Zoom meeting link and password to all the students registered for the course, by email -- using the email address they have on the UCB classes registration system. The students who are NOT officially registered, and wish to be included in this email list, should send me an email asap, and I will add them to the list. I have sent a first test email with more info before noon today (3/11/20), please check whether you received it.

In our first lecture on AdS/CFT (on 3/12/20), we will be (more or less) following Maldacena's elegant and insightful TASI lectures,
J.M. Maldacena, TASI 2003 Lectures on AdS/CFT, arXiv:hep-th/0309246.

Update (after the March 12 online lecture): Thank you everyone for participating in our first online lecture, and for your patience with the process and my learning curve with Zoom. Here are some additional references on the material we discussed today:
The holographic principle originated from the following two papers:
G. 't Hooft, Dimensional Reduction in Quantum Gravity, gr-qc/9310026,
L. Susskind, The World as a Hologram, hep-th/9409089.
The large N expansion of a quantum field theory of matrix degrees of freedom as being equivalent to string theory:
G. 't Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B72 (1974) 461.
The solution of this problem in 1+1 spacetime dimensions:
G. 't Hooft, A Two-dimensional Model for Mesons, Nucl. Phys. B75 (1974) 461.
The original idea for using a large N expansion in stat-mech and lattice models was published is a 3-pages long paper
H.E. Stanley, Dependence of Critical Properties on Dimensionality of Spin, Phys. Rev. Lett. 20 (1968) 589.
The founding paper of AdS/CFT correspondence has now more than 15,000 citations:
J.M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, arXiv:hep-th/9711200.
In retrospect, it was very wise to ask the questions about large N duality first for the simplest quantum field theories: those that have (super)conformal symmetry, and therefore represent fixed points of the renormalization group. The fact that maximally suppersymmetric Yang-Mills in 3+1 theories is a superconformal theory was first shown (in Berkeley!) by Stanley Mandelstam, in lightcone gauge:
S. Mandelstam, Ligh-Cone Superspace and the Ultraviolet Finiteness of the N=4 Model, Nucl. Phys. B213 (1983) 149.

Our next online lecture will be on Tuesday, March 17, 12:30pm as usual. I will send the Zoom link sometime before Monday evening to our extended email list.

Week 9: Update (3/17/20): Yesterday I sent a group email with the recurring Zoom link for our Tuesday and Thursday classes, which should be our standard link for the rest of the semester. If you did NOT receive this Zoom link, or you wish to be added to the email list, please email me asap. See you all in today's class!
Update (3/20/20):This week in lectures we covered the introduction to AdS/CFT, and have been developing the bottom-up approach and the basics of the AdS/CFT dictionary, especially for the classic example of Type IIB superstring on AdS5 x S5, versus N=4 supersymmetric Yang-Mills in 3+1 dimensions. The main reference is still the Maldacena TASI lectures.
In addition, I wanted to post two more references: First, the comprehensive early review paper on AdS/CFT, in which many introductory details are developed very explicitly:
O. Aharony et al., Large N Field Theories, String Theory and Gravity, arXiv:hep-th/9905111;
and the link to the exciting new book from some of the "founding fathers" of AdS/CMT correspondence. This book has just been published by MIT press, but it has a great early version in arXiv, with a link in the Comments to the MIT press webpage of the actual book:
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic Quantum Matter, arXiv:1612.07324.

Update about the timeline for your Reading Assignments, and our schedule for Spring break: Given the challenging circumstances for everyone, I have decided to run the Reading Assignment via email, with no personal presentations from the students. This weekend as our Spring break begins, I will post a list of about 25 papers. You will look through them at your convenience during the break. On Monday, March 30, starting from 2:00pm PDT, you can email me your request for your 1st choice paper to be assigned to you. (Please don't ask for your choice earlier; all early requests will be ignored :) I will assign your Reading Assignment paper on the first-come, first-served basis. Then you will have weeks to read the paper, you prepare a pdf file summary of your understanding of the main point(s) of the paper, and towards the end of the semester I will ask you to email it to me (and the group). This will satisfy my formal requirements on the students for this course. All students are then encouraged to read everybody else's 2-page summary, and initiate discussions of related physics questions, either via communicating with me or with other students directly by email, Zoom etc.
Spring break: Our online lectures will formally resume after Spring break, on Tuesday, March 31. However, I will keep our regular Tuesday and Thursday Zoom meetings at 12:30pm active even during Spring break -- please feel free to check in, chat about physics and boost everybody's morale during these trying times. No systematic new material will be introduced by me during these two Spring break Zoom meetings, and our systematic discussion of AdS/CFT will resume after the break.
As always, please feel free to email me with any questions, suggestions etc. Stay strong, resilient and healthy!

Week 10: Spring break.
Update (3/23/20): I am still working on the list of Reading Assignments to be posted. I will try to post it before the end of the day today.
Update (evening of 3/23/20): The list of available Reading Assignments has been posted here.

Update (3/26/20): Today in our informal discussion, I was asked about the importance (or not) of boundary terms in QFT and quantum gravity. Here are some references for boundary terms and boundary conditions in classical general relativity:
The famous addition of "Gibbons-Hawking" (=trace of the extrinsic curvature) boundary terms to the variational principle of classical general relativity goes back to two papers:
J.W. York, Role of Conformal Three-Geometry in the Dynamics of Gravitation, Phys. Rev. Lett. 28 (1972) 1082,
and
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D15 (1977) 2752.
For additional aspects, see for example
S.W. Hawking and G.T. Horowitz, The Gravitational Hamiltonian, Action, Entropy, and Surface Terms, arXiv:gr-qc/9501014.
For a nice and useful recent discussion of the issue of boundary conditions in the Euclidean-signature path integral for gravity, see:
E. Witten, A Note on Boundary Conditions in Euclidean Gravity, arXiv:1805.11559.
For a flavor of some additional active recent discussions of the boundary terms in classical and quantum gravity, see for example the following paper and the references therein:
S. Chakraborty, Boundary Terms of the Einstein-Hilbert Action, arXiv:1607.05986.
Another very classic paper involving boundary conditions in quantum gravity, which was ahead of its time by perhaps 10 or more years, is definitely worth reading now, and in fact it is a preview of what we will see later in this course when we talk about holographic renormalization:
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207.

Week 11: We are back from Spring break, thankyou to all the students who chose to check in for our regular Tuesday and Thursday Zoom meetings even during the break. This week we have resumed the systematic discussion of the dictionary of the AdS/CFT correspondence, putting more flesh on the bones of the basic duality relations.
Update (4/2/20): Since Monday, March 30, the students can inform me of their selection from the posted list of Reading Assignments, and most students have already chosen their paper. If you are registered for the course and have not sent me an email with your selection, please do so in the next few days, or let me know if you experience any technical difficulties.

Week 12: This week, we wrapped up the basics of the bottom-up approach to AdS/CFT holography and its generalizations, discussing the theory at finite temperature, correlation function of observables including Wilson loops, and examples of the holographic geometrization of confinement. Then we talked about holographic renormalization, specifically in the context of nonrelativistic versions of AdS/CFT correspondence, for Lifshitz-type field theories with anisotropic scaling. Our discussion of this topic was based on my lecture notes from the 54th Schladming Winter School in 2016, especially the 2nd lecture, on Nonrelativistic Holography and Holographic Renormalization,
the pdf file of that lecture can be found here.
(The full list of lectures at that Schladming Winter School can be found here.)
The technique of holographic renormalization in the special case of relativistic systems is well covered by various excellent lecture notes, for example in
K. Skenderis, Lecture Notes on Holographic Renormalization, arXiv:hep-th/0209067,
and
J. de Boer, The Holographic Renormalization Group, arXiv:hep-th/0101026.
In the lectures on nonrelativistic holography, we focused on nonrelativistic systems whose renormalization-group fixed points are of the "Lifshitz type" (they symmetries contain the spacetime isometries and an anisotropic scale transformation). For holography of nonrelativistic systems of the "Schroedinger type" (with an additional U(1) symmetry, which can be associated with a conserved particle number), see for example:
S. Janiszewski and A. Karch, Nonrelativistic Holography from Hořava Gravity, arXiv:1211.0005.
At the end of this week, we started our top-down re-derivation of the canonical example of AdS/CFT correspondence from D3-branes in Type IIB superstring theory.

Week 13: First, we will complete the top-down derivation of AdS/CFT from superstring theory. (A detailed discussion of the various steps in this derivation can be found for example in Chapter 5 of the book by Ammon and Erdmenger, cited above. For another good pedagogical source, see Polchinski's 2010 TASI lectures:
J. Polchinski, Introduction to Gauge/Gravity Duality, arXiv:1010.6134.)
Then, we move on to the next main topic of the lectures: Cosmological inflation, first phenomenologically in the bottom-up approach involving effective field theory methods, followed by a brief discussion of possible top-down approaches to inflation in string theory. Our standard reference is the book by Baumann and McAllister, cited above. (Much of this book can be found in the arXiv, here:
D. Baumann and L. McAllister, Inflation and String Theory, arXiv:1404.2601.)

Week 14: Phenomenology of inflation. Besides the textbook cited above, here are some of my favorite resources on this subject that complement the book but still use the same language:
D. Baumann, TASI Lectures on Inflation, arXiv:0907.5424,
see also Daniel Baumann's lecture notes, currently at UvA. (There used to be a DAMTP link to an earlier version of those, can't find it.)
And for a more introductory background on modern cosmology, I recommend the following textbooks:
S. Dodelson, Modern Cosmology (Academic Press, 2003) (apparently, a much expanded 2nd edition is coming up :) ,
V. Mukhanov, Physical Foundations of Cosmology (Cambridge U.P., 2005),
and the more theoretical
V. Mukhanov and S. Winitzki, Introduction to Quantum Effects in Gravity (Cambridge U.P., 2013).
Finally, the ultimate book on cosmology, and my hands-down all-time favorite on the subject, is
I. Calvino, The Complete Cosmicomics (Houghton Mifflin Harcourt, 2014).
Here is a link to Ursula Le Guin's 2009 review of this book (written at the time when this ultimate collection first appeared in English in the UK).

Week 15: Effective field theory of inflation. Technical Naturalness in EFT and inflation. Leading puzzles of Naturalness: The cosmological constant problem, the Higgs mass hierarchy problem, ... , and the eta problem in inflation.
Update on Reading Assignments: The two-page typed summaries of your selected Reading Assignment are due this Thursday, April 30, by midnight -- please email the pdf files directly to me.

Next week will be RRR week, and as in our 234A course last semester, I will continue lecturing through RRR week on our regular times on Tue and Thu. We will talk about the nonequilibrium QFT formalism (a.k.a. Schwinger-Keldysh formalism), its uses in inflation, and its possible role in string theory.

horava@berkeley.edu