String/M theory, Master course, 7.5p, Lp IV 2008
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2008: Tuesday 1 April at 15.15 in Origo 6115
(the physics building called Origo, 6th floor, north wing).

Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C

Literature:
Required: "Supersymmetry in particle physics", Ian Aitchison, (Cambridge university press 2007).
Available for about 500 SEK at Cremona.

Recommended: "A first course in string theory", Barton Zwiebach, (Cambridge university press 2004).
Available on the net for < 600 SEK, and at Cremona.

Tentative study plan for the course:
week 1 (calender week 14): Aitchison Chapter 1
week 2 (calender week 15): Aitchison Chapter 2, 3 and 4
week 3 (calender week 16): Aitchison Chapter 5 and 6
week 4 (calender week 17): Aitchison Chapter 7 and 8
week 5 (calender week 18): Aitchison parts of Chapter 9-12
week 6 (calender week 19): Zwiebach Chapters 1-3, and parts of 12 and 13
week 7 (calender week 20): Zwiebach Chapter 14
week 8 (calender week 21): Zwiebach Chapter 15
week 9 (calender week 22): Summary lecture and oral exams

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DETAILED STUDY PLAN FOR THE WEEKS 1-9 (CALENDER WEEKS 14 TO 22)

NOTE: The links below suggest extra reading material that is not included in the course requirements
and will not appear in the oral exam (unless the article is used in a home exam problem).
NOTE: The exercises in the text called "Quick calculations" in Zwiebach and the ones
denoted "Exercise" in Aitchison are generally very nice and give a good check that you have
understood the material. In the chapters included in the course, you should try to do them without exception.
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Schedule: All lectures in Origo 6115
Tuesdays at 15.15-17.00
Thursdays at 10.00-11.45
The time for the third lecture will change from week to week:
Fridays at 10.00-10.00
or
Wednesdays at 10.00-12.00

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1st week (calender week 14): Introduction and basic aspects from field theory

To read: Aitchison Chap 1 and lecture notes
Lectures
1: Tuesday April 1, at 15.15: Units, Maxwell´s equations, the path integral
2: Thursady April 3, at 10.00: propagators, the Dirac equation, QED scales, renormalized coupling constant
3: Friday April 4 at 10.00: hadrons, non-abelian gauge symmetry, QCD and its renormalized couplings

Home problems:
Hp1: Use the path integral method (see Peskin page 289-292) to derive the Feynman rules for massive \Phi^3 theory.
Hp2: Derive the covariant derivative and the field strength for a general gauge group G. Find the transformation
rules for the gauge field and the field strength in terms of a group element \bar{g} and the corresponding
variations to lowest order in the (infinitesimal) gauge parameter (by writing \bar{g} as an exponential,
calling the generators T^a which is more standard than J^i).

Dead-line: April 18

Further reading:
That the start of LHC is stirring up interest and emotions among the public is clear from "LHC in US lawsuit".
(An excellent but a bit more advanced account of large extra dimensions and microscopic black holes
can be found in "this article by Kanti".)

A more scientific discussion is the fact that String/M theory introduces extra dimensions.
Have a look at the history of such by reading Stanley Deser's account "The many dimensions of dimension",
and the first few pages in the article "Perspectives on issues beyond the standard model" by G. Kane.

For a recent discussion of units and fundamental constants in nature, see Mike Duff
"Comment on time variation of fundamental constants ".
and for comments on extra dimensions, read the first three or four pages in F. Ferugio's review article
"Extra dimension in particle physics".

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2nd week (calender week 15): Introduction to supersymmetry

To read: Aitchison Chap 2 and lecture notes
Lectures
4: Tuesday April 8, at 15.15: Problems in the weak sector, Lorentz symmetry, spinors
5: Wednesday April 9, at 10.00: Spinors; cont. from previous lecture
6: Thursday April 10 at 10.00: cont. from previous lecture

In the article " Naturally Speaking: The Naturalness Criterion and Physics at the LHC "
you may find more non-technical discussions on hierarchy and fine-tuning problems.
You may also find some nice reading about the very interesting person Ettore Majorana in
" Majorana and his heritage seventy years later"

Home problems:
Hp3:i)Insert the VEV (vacuum expectation value) of the Higgs doublet into its kinetic term
written in terms of the appropriate covariant derivative and verify that out of the four
electro-weak gauge fields, three get a mass and one remains massless (the photon).
ii) Do the same with a generic lepton Yukawa term, i.e. an interaction term involving one left-handed
doublet lepton field, one singlet right-handed lepton field, and the doublet Higgs scalar.
Use Dirac spinors and projection operators P_{L} and P_{R}. Check that the correct field gets massive.
Verify that the projection operators are OK, i.e. that they do not make the Yukawa term vanish.
Hp4:i) Prove that C\gamma^{\mu\nu} is symmetric.
ii) Consider the spin 1 and spin 1/2 generators of the Lie algebra SO(1,3) given in lecture 6.
Verify that they satisfy exactly the same algebra (i.e. normalized in the same way).
iii) Check that this spin 1/2 generator is consistent with the equations (2.17) and (2.18) in Aitchison.
Dead-line: April 25

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3rd week (calender week 16): Basic supersymmetric models

To read: Aitchison Chap 3-5 and lecture notes
Lectures
7: Tuesday April 15, at 15.15:chap 2: Lecture and Exercise class on spinors
8: Wednesday April 16, at 10.00: A simple supersymmetric model
9: Thursday April 17 at 10.00: The supersymmetry algebra and auxiliary fields.
10: Friday April 18 at 10.00: Chap 5.1: The interacting theory.

Home problems:
Hp5:Derive the real Majorana form of the chiral version of the Lagrangian for the WZ-model.
Hp6:Complete the calculation from the lecture showing that the commutator of two
supersymmetry transformations on the spinor field \chi_a closes off-shell when the auxiliary field F is
incorporated into the calculation.
Dead-line: May 6

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4th week (calender week 17): The vector multiplet

To read: Aitchison Chap 5.2, and 7 (Chap 6 is not included in the course)
Lectures
11: Tuesday April 22, at 15.15:chap 2: Wess-Zumino quantum corrections
12: Thursday April 24 at 10.00: The vector multiplet.

Home problems:
Hp7 :Derive the B-loop tadpole correction to the A-propagator using the path integral.
Hp8 :Show that the susy variation of the abelian vector gauge field is a real
expression, i.e. not complex.
Dead-line: May 9

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5th week (calender week 18): The MSSM

To read: Aitchison Chap 8 and parts of Chap 9.
Lectures
CANCELLED: Monday April 28, at 10.00:Chap 8: The MSSM.
13: Friday May 2 at 10.00: Chap 8: The MSSM and some points from Chap 9 on SUSY breaking.

Home problem:
Hp9 :Explain the result in Aitchison eq 8.82 in full detail. This positive result relies
partially on the fact that MSSM must contain at least two Higgs doublets. Explain why one doublet is not a possibility.
Dead-line: May 16

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6th week (calender week 19): Introductory string theory

To read: Zwiebach Chaps: 1, 5, 6.1-6.2, 6.3-6.7 and the results of 6.9.
Zwiebach Section 21.6, page 122 in Sect. 7.3 and sect. 7.4
Sections 9.3-9.5.
Lectures
14: Tuesday April 6, at 15.15:
15: Wednesday April 7, at 10.00:
16: Thursday April 8 at 10.00:

Home problem:
Hp10 :Solve problems 5.5 and 5.6 in Zwiebach.
Hp11 :Solve problem 9.3 in Zwiebach.
Dead-line: May 23

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7th week (calender week 20): The quantum string theory

To read: Zwiebach 21.1-12.2, 12.4-12.6, 13.1-13.4.

Lectures
17: Tuesday April 13, at 15.15:
18: Wednesday April 14, at 10.00:
19: Thursday April 15 at 10.00:

Home problem:
Hp12 :Solve problem 12.7 in Zwiebach.
Hp13 :Solve problem 12.10 in Zwiebach.
Dead-line: May 23

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8th week (calender week 21): D-branes and LHC physics

NOTE: The oral exams are next week! Please book a time as soon as possible.

To read: Zwiebach Chaps 14 and 15.

Lectures
20: Tuesday April 13, at 15.15:
21: Wednesday April 14, at 10.00:
22: Thursday April 15 at 10.00:

Home problem:
Hp14 :Solve problems in Zwiebach.
Hp15 :Solve problem in Zwiebach.
Dead-line: The solutions should not be handed in, but the oral exam might contain
questions related to these probelms

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9th week(calender weeks 22): Examination week

Examination:Please schecule the oral exam with me a soon as possible.
The last day possible for the oral exam is Wednesday May 30.

NOTE: Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points
4 requires 60% of the total points
5 requires 80% of the total points plus a successful oral exam

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About this home page: Below the home page will contain more detailed information about the material
covered each week but note that this information is added to the home page as the course proceeds.
Please let me know if you have ideas and suggestions for improvements of this home page!

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Additional reading:

Non-technical string literature: An excellent popular account of the fundamental questions and
ideas of modern string/M theory can be found in
"The elegant universe", by Brian Greene (Jonathan Cape 1999).

General high-energy physics:
A very nice overview of elementary particle physics, gravitation and cosmology, Kaluza-Klein,
supersymmetry and introductory string theory can be found in
"Particle physics and cosmology", by P.D.B. Collins, A.D. Martin and E.J. Squires (Wiley 1989).

Recent books debating the pros and cons of string theory
L. Smolin, "The trouble with physics" (Houghton Mifflin Company, 2006)
P. Woit, "Not even wrong" (Jonathan Cape, 2006)
see also comments on these by J. Polchinski:
Guest Blogger: Joe Polchinski on String Debates

Literature discussing unification and reductionism
"Dreams of a final theory", Stephen Weinberg (Vintage 1992): Very good!!
"The emperor's new mind", Roger Penrose (Penguin 1989)

Some articles from Physics Today:
Witten, Physics Today, April 1996, p. 24-30
Kane, Physics Today, Febr 1997, p. 40-42
Collins, Physics Today, March 1997, p. 19-22
Witten, Physics Today, May 1997, p. 28-33

Additional (advanced) string literature: (abbreviation in bracket)
1. M. Green, J. Schwarz and E. Witten (GSW), "Superstring theory", volume I and II (Cambridge University Press 1987).
2. J. Polchinski (JP), "String theory", volume I and II (Cambridge University Press 1998).
3. D. Lüst and S. Theisen (LT), "Lectures on string theory", (346 Lecture Notes in Physics, Springer Verlag 1989).
You can find the book here as Part 2, Part 3. "Part one",
4. C. V. Johnson, "D-branes" (Cambridge monographs on mathematical physics 2003)
5. K. Becker, M. Becker, and J.H. Schwarz (BBS), "String theory and M-theory",
(Cambridge Univ Press 2007)

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About the books recommended for this course

The 2008 version of the Master course String/M theory is revised
to meet the growing excitement due to the start of the LHC (Large Hadron Collider)
at CERN later this year or early next year. As a result the string theory course will start by
going through the very pedagogical and nice account of the supersymmetric version
of the Standard Model in the book by Aitchison. The book is presenting the
normally rather heavy formalism of supersymmetry in a very down to earth way
giving the student the best possible guidance through this material.
The result is a good understanding of what we are looking for at LHC
in terms of Higgs physics and supersymmetry.

The third thing searched for at LHC is extra dimensions.

The book "A first course in string theory" by Barton Zwiebach provides an
extremely pedagogical introduction to this very stringy subject
by starting from physics familiar to all undergraduate students having
studied physics for two years at the university. The required knowledge of
mathematics is kept at a minimum by providing detail explanations of all
the mathematics used that is not part of the first year mathematics
curriculum.
All the necessary aspects of field theory, from electromagnetism to gravity,
and quantum mechanics are explained from scratch and developed just to the
level needed for the applications in question.

A large number of exercises and problems appear in each chapter of both books
some of which will be used as home exam problems for this course.

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Examination:
Home problems and a successful oral exam for highest mark (CTH: 5, GU: VG)

Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points plus an oral exam
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points plus an oral exam
4 requires 60% of the total points plus an oral exam
5 requires 80% of the total points plus a successful oral exam

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