lect2

General info	Program	Participants	Registration	Fee & Grants	DIAS-TH
Advanced Summer School on Modern Mathematical Physics Dubna, July 14-26, 2005
main	travel	weather	visas

I. Buchbinder (Tomsk)
Introduction to Supersymmetric Field Theory (6 lectures)

1. General physical idea of supersymmetry. Lorentz and Poincare groups. Two-component spinors. Lie algebra of Poincare group and its irreducible unitary representations.

2. Superalgebra. Irreducible representations of supersymmetry. Elements of algebra and analysis with anticommuting variables.

3. Superspace and superfields. Component structuire of superfield. Supersymmetry generators and supercovariant derivatives. Chiral and general scalar superfields.

4. Field theory in superspace. Wess-Zumino model. Supersymmetric sigma-model. Supersymmetric gauge theories.

5. Supersymmetric quantum field theory. Superfield perturbation theory. Superpropagators. Supergraphs.

6. Renormalization of supersymmetric field theories. Supersymmetric background field method. Nonrenormalization theorem. Superfield effective potential.

Training session leaders : I. Samsonov

E. Ivanov (Dubna)
Introduction to Extended Supersymmetry

Lecture 1. Extended SUSY: motivations and uses. Coleman-Mandula no-go theorem and how to evade it. Representations on one-particle states: massive and massless. Self-conjugated multiplets and N=8 barrier. Extended SUSY in 4D via dimensional reduction from $D > 4$. Field theory realizations, physical and auxiliary fields.

Lecture 2. Superspaces of N=2 SUSY: conventional and harmonic. Merits of off-shell superfield formulations. Grassmann harmonic analyticity as the true N=2 analog of N=1 chirality. N=2 hypermultiplet on shell and off shell, infinite number of auxiliary fields as a price for off-shell unconstrained formulation. Most general hypermultiplet action and hyper K\"ahler sigma models.

Lecture 3. Geometric principles underlying N=0 and N=1 gauge theories. N=2 SYM theory from preserving harmonic analyticity. Wess-Zumino gauge. Superfield and component actions. Maximally extended N=4 SYM theory in N=2 superfield formualtion.

Lecture 4. Elements of quantum theory in harmonic superspace. Fixing the gauge, superfield FP ghosts, vertices and propagators. Simplest Feynman supergraphs. Basic idea of non-renormalization theorems.

Lecture 5. Supergravity as supersymmetrization of Einstein theory. Questions to be answered. N=1 supergravity, the method of conformal compensators. From conformal N=2 SG to N=2 Poincar\'e SG. Maximally extended N=8 SG.

Lecture 6. N=3 harmonic analyticity. The N=3 SYM off-shell action as the harmonic analog of Chern-Simons action. Ultraviolet finiteness made manifest.

Olaf Lechtenfeld, Christian Saemann & Martin Wolf (Uni. Hannover)
Twistors, Supersymmetric Gauge Theory and Integrability

Lecture 1 (90 min.) : The twistor construction (Christian Saemann)
- basics of complex geometry
- twistor space, flag manifolds, twistor correspondence
- Penrose transformation
- supermanifolds

Lecture 2 (90 min.) : Twistor gauge fields (Martin Wolf)
- (self-dual) super Yang-Mills actions
- Penrose-Ward transformation
- holomorphic Chern-Simons theory
- relation with topological B-model

Lecture 3 (90 min.) : Twistor string fields (Olaf Lechtenfeld)
- basics of string field theory
- open N=2 strings
- Berkovits-Siegel string field theory
- cubic supertwistor N=2 string field theory

G. Lopes Cardoso (Munich)
Supersymmetric Black Holes
We give an introduction to extremal black holes in supergravity and in string theory. The macroscopic entropy of these supersymmetric black holes is computed using Wald's definition of black hole entropy. This entropy exhibits subleading corrections which originate from higher-order curvature terms on the supergravity side. We discuss the attractor mechanism, which ensures that the macroscopic entropy depends only on the charges carried by the black hole. We show that for certain types of black holes, the macroscopic entropy based on Wald's definition can be microscopically reproduced by a state counting in string theory.

D. Sorokin (Padova)
Relativistic particles and strings
1. Introduction.
Classical dynamics of relativistic point-like and extended objects (particles, strings, membranes, p-branes).
The geometrical structure of actions and equations of motion of
- bosonic particles, strings, p--branes;
- spinning particles and strings;
- superparticles, superstrings and super-p-branes.

2. Symmetries, constraints and quantization of the dynamics of relativistic objects
- the Dirac analysis;
- quantization and the quantum spectrum of bosonic and spinning particles;
- kappa-symmetry and the problem of covariant quantization of superparticles.

3. Bosonic string theory
- action, symmetries, equations of motion
- constraints
- conformal invariance

4. Canonical quantization of the bosonic string
- gauge fixing and the conservation of the string symmetries in quantum theory
- quantum anomalies and the critical dimension of space--time

D.Vassilevich (Uni. Leipzig)
Supersymmetric Solitons
1. Introduction, Bogomolny equations, supersymmetry, central charge.
2. Quantum corrections to susy solitons, naive vs precise calculations, anomaly in the central charge.
3. Supersymmetry and boundaries.

Y. Shnir (Oldenburg)
Supersummetric monopoles and related topics
(i) SU(2) multimonopoles and moduli space approximation;
(ii) SU(N) generalization (minimal and maximal symmetry breaking and massless monopoles etc)
(iii) N=2 SUSY SU(N) monopoles (BPS bound revisted, 1/4 BPS monopoles, low-energy dynamics etc)

M.Vasiliev (LPI, Moscow)
Intruduction into higher-spin theory (5 lectures)
An elementary introduction into theory of higher spin gauge fields will be given. A particular emphasize will be on the MacDowell-Mansouri formulation of gravity in anti-de Sitter space and its generalization to the case of higher spin gauge fields. The related concepts such as Young tableaux, star product and unfolded formulation of dynamical systems will be introduced.

Training session leaders : O. Shaynkman*, K.Alkalaev, A. Matveev*, S. Didenko*
* to be confirmed