Winter 2005

Feb 9:Sam Pinansky: Solving Seiberg Witten Prepotentials using instantons
I will review the ADHM construction of instantons for SU(N) N=2 Supersymmetric Yang Mills theory, and then use a topological twist to localize the integral over instanton moduli space. Then I will evaluate that integral, giving an expansion of the Seiberg Witten prepotential without any reference to string theory based on the work of Hollowood. I will then do the exact same thing in the language of algebraic geometry based on the work by Nekrasov.

References:
---hep-th/0206063 "The calculus of many instantons" <- A gargantuan review of instantons
---hep-th/0201075 "Calculating the Prepotential by Localization on the Moduli Space of Instantons"
---hep-th/0404225 "ABCDs of instantons"
---hep-th/0306238 "Seiberg Witten Theory and Random Partitions"
---hep-th/0306211 "Seiberg Witten Prepotential from Instanton Counting"
Meeting: 4pm small seminar room. Email: samuelp@physics.ucsb.edu


Feb 2:Mads Fransden: Planar Equivalence and its Implications
In this talk I will review Shifman et al's article on planar equivalence: Planar equivalence is a common term for the large-N equivalence of certain sectors of certain theories arising from e.g orbifolding a `parent` theory to obtain a daughter!. In this talk I will focus on and 'prove' the non-perturbative equivalance of (part of) the bosonic sector of N=1 Super Yang-Mills and a theory of one massless dirac-fermion in the asymmetric representation (orientifold-A theory). This theory has the very interesting feature that for N(color)=3 it is simply massless 1 flavor QCD! Thus our main motivation for this gymnastics is to calculate and analyze nonperturbative quantities in (almost!) QCD by importing known stuff from SYM...and vice versa! I will mention examples of this at the end. An important part of the above `proof` is the large-N factorization of Wilson-loops so I will discuss large-n gauge theory in general and argue this property following Makeenkos really good review closely.

References:
---A.Armoni, M.Shifman, G.Veneziano hep-th/0403071
---M.Makeenko hep-th/0001047
Meeting: 4pm kITP auditorium. Email: madstf@hotmail.com


Jan 28:Henriette Elvang: Boundary Terms in GR and Designer Gravity
The talk takes off with a brief discussion of Hamiltonian formalism in General Relativity, boundary terms and boundary conditions. First we'll consider asymptotically flat spacetimes, but we'll then move on to spacetimes which are asymptotically AdS. We'll focus on gravity coupled to a scalar field, discuss boundary conditions and the Breitenlohner-Freedman bound. This all leads up to "designer gravity": how to design AdS solitons by specifying certain boundary conditions on the fields. We'll comment on the interpretation in the context of the AdS/CFT correspondence.

Some references:
- Hamiltonian formalism in GR: Wald, appendix E.
- AdS boundary condition: Henneaux and Teitelboim "Asymptotically Anti-de Sitter Spaces", Commun. Math. Phys. 98 (1985) 391.
- Designer gravity: Hertog and Horowitz, "Designer Gravity and Field Theory Effective Potentials", hep-th/0412169.
Meeting: 4pm small seminar room. Email: elvang@physics.ucsb.edu


Jan 19:Jacopo Orguera:The Berkovits-Witten Twistorial String Theory
Roger Penrose invented Twistor space in order to quantize spacetime, although that goal has not been achieved this particular formalism has proven to be very powerful. The space is defined as the set of light ray of the physical space and therefore any theory formulated in twistor space admits only massless spectrum. This is a clear limitation; however when used as a toy space for string theory it can offer some very nice results; for example we will show how string theory in (super)twistor space is equivalent to N = 4 superconformalgravity + N = 4 SUSY in spacetime. Most of the recent literature on the subject use results from tree level string theory (which is equal to SUSY) in order to obtain other field theory amplitudes (ie in QCD) via a mixed formalism. We will not deal with this very interesting and dynamic topic, we will focus on the theoretical foundations of string theory in twistor space. I'll do my best to be self contained.

References:
---hep-th/0406051 Nathan Berkovits, Edward Witten "Conformal Supergravity in Twistor-String Theory"
---hep-th/0312171, Perturbative Gauge Theory As A String Theory In Twistor Space, Edward Witten
---hep-th/0403047, MHV Vertices And Tree Amplitudes In Gauge Theory, Freddy Cachazo, Peter Svrcek, Edward Witten
---hep-th/0403199, Parity Invariance For Strings In Twistor Space,Edward Witten
Meeting: 4pm small seminar room. Email: jacorg@physics.ucsb.edu


Jan 12:Sam Vazquez: Giant Gravitons in AdS/CFT
In this talk I will explain how D-branes arise as a subsector of the 1/2-BPS operators of SYM theory. First I will review how the 1/2-BPS sector of the theory can be described as a single matrix quantum mechanics. Then, I will concentrate in operators that are dual to D-branes in $AdS_5\times S^5$, the so-called "Giant Gravitons". We will see how to incorporate the geometrical fluctuations of these branes in the SYM side, and how these give rise to open strings in certain limits. Furthermore, by calculating the anomalous dimension matrix, one is able, in principle, to write down a Hamiltonian (in the string theory side) that describes highly non-perturbative physics of D-branes of different sizes mixing with each other, transitions between D-branes and closed strings, etc. I will explicitly discuss a part of that Hamiltonian that describe states with only two angular momenta in the $S^5$. Then by taking a large-charge limit, I will show how one obtains a sigma model describing open semiclassical strings with Dirichlet boundary conditions in the Giant Gravitons.

References:

Part of my talk will be based on the research that I'm working on at this moment with Dr. Berenstein and Dr. Correa. Therefore, there are no references for that (yet). The following references cover the early appearence of giant gravitons in the literature [1 - 3], the 1/2-BPS states of SYM theory [4] and, finally a nice recent paper giving evidence on how an emergent gauge symmetry arises from the open strings ending in coincident giant gravitons [5]. This paper also discusses how add fluctuations to the D-branes, how to find the operators describing many D-branes, etc.

[1] John McGreevy, Leonard Susskind and Nicolaos Toumbas, "Invasion of the Giant Graviton from Anti de Sitter Space", hep-th/0003075.
[2] Marcus T. Grisaru, Robert C. Myers, Oyvind Tafjord, "SUSY and Goliath", hep-th/0008015.
[3] Akikazu Hashimoto, Shinji Hirano, N. Itzhaki, "Large Branes in AdS and their Field Theory Dual", hep-th/0008016
[4] David Berenstein, "A Toy Model for the AdS/CFT Correspondence", hep-th/0403110.
[5] Vijay Balasubramanian, David Berenstein, Bo Feng, Min-xin Huang, "D-branes in Yang-Mills Theory and Emergent Gauge Symmetry", hep-th/0411205.
Meeting: 4pm small seminar room. Email: astrosam@physics.ucsb.edu