Fall 2003

Oct 8: Nick Jones: Calculations in Boundary String Field Theory and Sen's conjectures
Tachyon effective actions provide direct and exact means to verify Sen's conjectures. Motivating the BSFT formalism by deriving the DBI from a disc partition function, I'll explain the formalism, derive some exciting tachyon effective actions, and show how it is almost trivial to verify Sen's conjectures from them.

References:
--Witten, "On background independent open string field theory," hep-th/9208027
--Witten, "Some computations in background independent off-shell string theory," hep-th/9210065
--Kutasov, Marin~o, Moore, "Some exact results on tachyon consensation in string field theory," hep-th/0009148
--Kutasov, Marin~o, Moore, "Remarks on tachyon condensation in superstring field theory," hep-th/0010108.
--Kraus, Larsen, "Boundary string field theory of the DD-bar system," hep-th/0012198
Meeting:4:00pm small Seminar room. Email: nick.jones@cornell.edu


Oct 3: Ilarion Melnikov: Supersymmetric Boundary Conditions for the N = 2 Sigma Model
We clarify the discussion of N = 2 supersymmetric boundary conditions for the classical d=2, N=(2,2) Non-Linear Sigma Model on an infinite strip. Our conclusions about the supersymmetric cycles match the results found in the literature. However, we find a constraint on the boundary action that is not satisfied by many boundary actions that appear in the literature.

References:
--Melnikov, Plesser, Rinke, hep-th/0309223
--Ooguri, Oz, and Yin,"D-branes on Calabi-Yau spaces and their mirrors," hep-th/9606112.
--Kapustin and Orlov, "Remarks on A branes, mirror symmetry, and the Fukaya category," hep-th/0109098.
--Lindstrom, Rocek, van Nieuwenhuizen, "Consistent boundary conditions for open strings," hep-th/0211266.
Meeting:3:00pm Main Seminar room. Email: lmel@cgtp.duke.edu


Sept.25, Oct 2: Nick Halmagyi: Topological Strings and Mirror Symmetry
I want to explain topological sigma models and mirror symmetry. I will take the point of view that a sigma model with a Ricci flat Kahler manifold as a target space, is just one example of an N=2 SCFT in two dimensions. So in order to explain the topological twist of the sigma model I will first explain the topological twist of the N=2 SCFT.

References:
hep-th/9702155 : Brian Greene's notes on CY's and all that. This has a nice presentation (in chapter 3/4) of N=2 SCA, chiral rings, spectral flow and sigma models. He does not discuss the topo' twist.

hep-th/9301088 : Nick Warner's notes on N=2 SCFT. First two chapters are very relevant to my talk. Does not discuss sigma models.

hep-th/9112056 : Witten's classic on topological field theory and mirror symmetry. By the end of my talk I hope you will understand why he twists the fermions into scalars and vectors.

"GEOMETRY AND QUANTUM FIELD THEORY: A BRIEF INTRODUCTION" B.R Greene and H. Ooguri in "Mirror Symmetry II" This is a nice introduction to the sigma model.

The very keen should read the Trieste lectures by Dijkgraaf-Verlinde-Verlinde. They deal with the general issue of topological field theories. The notes are not that well known and deal with much more stuff than I will talk about but if you are very keen you might want to look at them. Click here
First Meeting: 4pm Small Seminar room, Second Meeting: 4:30pm Main Seminar room. Email: halmagyi@usc.edu


Sept.18: Ted Erler: BRST formalism
I will discuss the BRST formalism from the perspective of classical constrained Hamiltonian systems. This is truly the fundamental way to think about the BRST construction but is sadly far from general knowledge. All those who seek a fundamental geometrical understanding of BRST techniques are strongly encouraged to attend.

References:
--Ted Erler, "Lecture notes on the BRST formalism"
--J.W. Van Holten, "Aspects of BRST Quantization," hep-th/0201124
--Henneaux and Teitelboim, "Quantization of gauge systems"
--Barnich, Brandt, and Henneaux, "Local BRST cohomology in gauge theories," hep-th/0002245
Meeting: 4pm Small Seminar room. Email: terler@physics.ucsb.edu


Sept.11: Ted Erler: Constrained Hamiltonian Systems: A Tutorial
In this lecture, after a brief review of constrained Hamiltonians and a discussion of quantization, I will give some physical examples to illustrate the formalism. We will see examples of both first and second class contraints, the Dirac conjecture, reducible gauge theories, gauge fixing, the Gribov problem, and Dirac brackets. Those wishing to benefit from this lecture are strongly encouraged to refresh their memory by looking over the references and talking to me.

References:
--Ted Erler, "Lecture notes on Constrained Hamiltonian systems"
--J.W. Van Holten, "Aspects of BRST Quantization," hep-th/0201124
--PAM Dirac, "Lectures of Quantum Mecanics"
Meeting: 4pm Small Seminar room. Email: terler@physics.ucsb.edu


Sept.4: Henriette Elvang: Supertubes
A supertube is a rotating cylindrical D2-brane which is supported against collapse by its angular momentum. In this talk, I'll give a pedagogical introduction to supertubes. I'll go through the world-volume analysis of the supertube, and I'll discuss the interpretation of supertube as 'charged' fundamental strings 'blown-up' to a tube by angular momentum. Also, I'll discuss the supergravity solution describing the back-reaction of the supertube on the metric. Finally, I may tell you some secrets about supertubes.

References:
--D. Mateos & P. K. Townsend: "Supertubes", hep-th/0103030
--R. Emparan, D. Mateos & P. K. Townsend: "Supergravity Supertubes", hep-th/0106012.
Meeting: 4pm Small Seminar room. Email: elvang@physics.ucsb.edu


Aug.28, Sept.2: Matt Lippert: Quantum Fields in Curved Space
References:
--Birrell & Davies, Quantum Fields in Curved Space, ch 3,8
--Jacobson, Introduction to Quantum Fields in Curved Spacetime & the Hawking Effect, gr-qc/0308048
--Giddings and Nelson, Quantum Emission from Two-Dimensional Black Holes, hep-th/9204072
--Wald, General Relativity, ch 14.1-3
--Hawking, Particle Creation by Black Holes, Comm. in Math. Phys. 43, 1975
Meeting: 4pm Small Seminar room. Email: lippert@physics.ucsb.edu


Aug.14: Anshuman Maharana: D-branes and Yang-Mills Theory
Abstract: The effective action describing low energy fluctuations of a D-p brane is a U(1) susy-gauge theory with some neutral matter living on the p+1 dimensional volume of the D-brane. The dynamics of this theory is described by the Born-Infeld action, which has in addition to the standard Maxwell term has other non-linear terms in the Lagrangian.The amount of information about string theory contained in this action is quite remarkable. Although it is supposed to describe just the low energy fluctuations it tells us about about D-F , D-D bound states , quatization conditions and string junctions. There are even calculations which provide evidence for the fact that open strings should end on D-branes. I will try give an overview of these ideas.

References:
Meeting: 4pm Small Seminar room. Email: anshuman@physics.ucsb.edu


July 10, August 7: Ted Erler: Constrained Hamiltonian Systems
Abstract: I will try to explain some fundamental theoretical structures underlying the Lagrangian and Hamiltonian formulations of systems with gauge invariance. In this lecture I will focus on the theory of "constrained Hamiltonian systems," a subject pioneered by Dirac in the 1950's. After a lightning review of the geometry of Hamiltonian mechanics, I will introduce the concept of the "constraint surface" and the associated first and second class constraint functions, and explain their relation to gauge invariance. I will explain how this geometrical picture can be derived more or less systematically from the Lagrangian, and hopefully, time permitting, will give a couple of examples.

References:
--Henneaux and Teitelboim, "Quantization of Gauge Systems"
--Dirac, "Lectures on Quantum Mechanics"
--Gitman and Tyutin, "Quantization of Fields with Constraints"

Meeting: 4pm Small Seminar room. Email: terler@physics.ucsb.edu