MU:MU08109 Gauge Fields and Strings

MU08109 Gauge Fields and Strings

Mathematical Institute in Opava
Summer 2011

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Course objectives

Introduction to the string theory methods.

Syllabus

Supersymmetric field theories, quotient spaces, the Atiyah--Hitchin manifolds, the Seiberg--Witten solution, the Donaldson theory, the Seiberg--Wittenův invariant, conformal field theory in two dimensions, the Polyakov formalism, the string spectrum, the BRST quantization, the critical dimension, the Riemann surfaces, tree-level amplitudes, one-loop amplitudes, modular invariance, superstrings, supersymmetry in various dimensions, D-branes, M-theory, conformal quantum field theory, string compactification, the Calabi-Yau manifolds. Algebraic geometry in string theory. Toric geometry, quantum geometry, strings in singularities, constructing branes from gauge theories.

Literature

recommended literature

M. Greene, J. H. Schwarz, E. Witten. String theory, vol I, II. info
J. Polchinski. String theory, vol I, II, III. info
B. Zwiebach. A first course in string theory. 2004. info
L.H. Ryder. Quantum Field Theory. 1996. info
M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

Teacher's information

Oral exam; further requirements to be specified in the course of the semester.