Lecture 26 Mar

Posted on 2008/03/25 by kiwinerd

Today we discuss BPS states, the Bogomolnyi bound, Kaluza-Klein reduction on the circle, and S-duality.  Here are my notes (BPS states and S Duality).

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Replacement Lecture

Posted on 2008/03/25 by kiwinerd

We will have an extra (replacement) lecture on

  • Monday, March 31st, at 2pm
  • Location TBA.
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No Lecture 21.Mar

Posted on 2008/03/20 by kiwinerd

Hi everyone,

Suddenly I realized that 21.Mar is a holiday … it’s Good Friday in the Christian calendar (which we apparently celebrate as a country and as a university).

I’d like to reschedule the missing hour. Please expect an email message from me with “poll” in the subject line; I’ll be using a neat little utility called Doodle to let the class pick a replacement timeslot.

Cheers,

Prof. P.

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Homework 4

Posted on 2008/03/18 by kiwinerd

Note: since you all found the first three homeworks relatively easy, this one (and the last) will be a bit longer and a bit tougher… :-)

New due date: Mon.31.Mar before 18:00 (6pm).

Question 1A Separated Dp-branes and an Op-plane

Z14.4

Question 1B More about orientifolds [*optional]

Z14.10

Question 2 Strings and the Kalb-Ramond field

Z15.6 and Z15.7

Question 3 String partition function and Hagedorn temperature

Z16.2 and Z16.5

Question 4 Hot strings, random walks, and black holes

A: Z16.9

B: Starting from the following metric

hw4a

it can be shown that the Hawking temperature is inversely proportional to the horizon radius of the black hole

hw4b

(a) Using the Stefan-Boltzmann law and the fact that a Schwarzschild black hole horizon is spherical, estimate the lifetime of the Schwarzschild black hole (in D dimensions) caused by emission of Hawking radiation.

(b) What is the physical endpoint of Hawking radiation for this type of black hole?

(c) What is the Black Hole Correspondence Principle and why is it relevant here?

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Lecture 19 Mar

Posted on 2008/03/14 by kiwinerd

Here are my [overcomplete] notes:

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Lecture 14 Mar

Posted on 2008/03/12 by kiwinerd

Today we talked about material Z-bach focuses on in Chapter 17. We explained in detail T-duality on closed and open strings propagating on R1,8 x S1, flat spacetime times a circle. The important bits were: (a) solving the string wave equation with oscillators plus pieces linear in tau and linear in sigma and deriving the mass formula; (b) physical properties of KK and winding modes; (c) T-duality as switching momentum with winding and inverting the circle radius in string units; (d) enhanced SU(2) gauge symmetry at the self-dual radius; (e) T-duality as changing D-brane dimension because it swaps D and N conditions with one another; (f) D-branes, open strings and Wilson lines.  T-duality: the first duality

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Lecture 12 Mar

Posted on 2008/03/07 by kiwinerd

Based on material in Chapter 14 of Zwiebach, we wrapped up the story of the mass of fundamental open strings stretched between stacks of Dp and Dq branes (StringsBetweenDpAndDqBranes). We also gave a first introduction to T-duality (IntroducingTduality).

Before Friday’s class, please study Section 16.1-16.3 of Z-bach on the Hagedorn temperature. Most importantly, please study Chapter 17 of Z-bach on T-duality for both closed and open strings (TdualityOpenClosedStrings). This chapter in particular is important for cementing the notion of T-duality of closed strings in our brains (heheh, not branes…). T-duality is particularly important intellectually in a course about string theory, because it was the first duality symmetry to be well- understood.

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How to find Prof Peet

Posted on 2008/03/07 by kiwinerd

If you need to find me, please check my approximate weekly timetable online and  identi.ca feed.

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Topic schedule post-break

Posted on 2008/03/07 by kiwinerd

20080227 (W): Building the superstring state space in light-front gauge. Closed superstrings. Open superstrings. Neveu-Schwarz (NS) and Ramond (R) sectors. Dilaton, Kalb-Ramond field. [Z.Ch.13]

20080229 (F): The gamma matrix algebra and Spinors in diverse dimensions D. The Fock space representation. Dimensionality of spinors 2[D/2]. [AWP notes; Polchinski appendix]

20080305 (W): Kappa symmetry, i.e., how to formulate the manifestly supersymmetric string theory action principle in light-front gauge. [GSW Ch.5.1,5.2]

20080307 (F): Parallel Dp-branes and the mass of open strings stretched between them [Z.Ch.14]

20080312 (W): Parallel Dp-branes and Dq-branes and the mass of open strings stretched between them. A beginning introduction to T-duality as (a) worldsheet Hodge duality on X-derivatives and (b) something that flips Dirichlet and Neumann boundary conditions on open strings while switching Kaluza-Klein modes with winding modes.

20080314 (F): Circle compactification and T-duality for closed and open strings. Enhanced SU(2) gauge symmetry at the self-dual radius. [Z.Ch.16-18, and AWP reviews]

20080319 (W): The string density of states and the Hagedorn phenomenon; Why strings carry NS-NS B-field charge; visualizing strings ending on D-branes. [ZZ15.1,15.2]

20080326 (W) : Dimensional reduction and the Kaluza-Klein procedure. Superstring duality: S-duality, M theory, the deerskin diagram. BPS states. The physical role of wrapped D-branes. [AWP reviews and notes]

20080328 (F): The Dark Side of String Theory: spacetime warpage caused by N>>1 D-branes. D-brane geometries – BPS and non-BPS. A brief introduction to the black hole entropy computation industry.

[N.B. all futures dates are tentative]

20080331 (M): The geometry of D3-branes and a brief introduction to the AdS/CFT Correspondence. [AWP reviews and notes]

20080402 (W) and 20080404 (F): Superstring cosmology: D-braney models of inflation. Flaws of Ekpyrotic Cosmology models. Why it’s so hard to produce tensor modes from string theory. … [AWP notes]

20080409 (W) and 20080411 (F): Derivation of the famous beta function equations of string theory.

[Study period: 20080414 - 20080418]

[Exam period: 20080421 - 20080509]

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Lecture 07 Mar

Posted on 2008/03/02 by kiwinerd

Today’s focus was how to calculate the mass of open strings stretched between Dp-branes. Specifically, we worked out the cases of

  • 1 Dp-brane, which has a U(1) Maxwell field (with some transverse scalars) living on it;
  • N Dp-branes, which have a U(N) non-abelian gauge theory (with some transverse scalars)  living on them.

The same technology will easily allow us next time to see how to do it for

  • N Dp- and M Dq-branes with p<>q.
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