%PDF-1.2 %���� Lectures 27-29, pages 347-402: Realizations of global symmetries and local order parameters, Wilson loop and area law criterion for confinement, magnetic disorder, abelian Higgs model in 1+1 and 2+1 dimensions, magnetic monopoles as instantons in 2+1 dimensions, spontaneous breakdown of Z_N global symmetry in SU(N) Yang-Mills theory 0000001669 00000 n In the classical theory, the collection of all Wilson loops contains sufficient information to reconstruct the … 0000001819 00000 n Diffusion of Wilson Loops When increasing size of loop in 4-dimensional Euclidean space as function of parameter t - ”time ”, value of the (untraced) Wilson loop carries out Brownian mo- tion on the group manifold,S3(SU(2)). 0000005959 00000 n trailer << /Size 121 /Info 104 0 R /Root 107 0 R /Prev 267839 /ID[
0000004583 00000 n Your use of the MIT OpenCourseWare site and materials is subject to our 0000006892 00000 n 106 0 obj << /Linearized 1 /O 108 /H [ 727 784 ] /L 270089 /E 7123 /N 23 /T 267850 >> endobj xref 106 15 0000000016 00000 n MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. These lecture notes form the material for the graduate course QFT 2, the second of three quantum fieldtheory courses inthe graduate program inHigh Energy Theory at the Institute of Physics in Belgrade. 0000001511 00000 n 0000005108 00000 n 0000000727 00000 n With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. 0000005778 00000 n The course presents the functional for-malism of Schwinger-Dyson equations, generating functionals and Feynman path integrals. 0000001489 00000 n A Wilson loop or Wilson line is an observable in (both classical and quantum) gauge theory obtained from the holonomy of the gauge connection.Hence if the gauge connection is given by a globally defined 1-form A, then the Wilson loop along a closed loop C is the trace of the path-ordered exponential?where is the “path-ordering operator” and Aμ are the components of the connection. In these lecture notes I give a brief pedagogical intro- duction to the methods used in nonperturbative inves- tigations of QCD and other gauge theories. Lecture 22: Computation of the Wilson Loop Flash and JavaScript are required for this feature.This is one of over 2,200 courses on OCW. 0000004691 00000 n In the dual string theory this is calculated by a string world–sheet in AdS5 × S5 ending along the two lines on the boundary (c). The motion of an ensemble of these degrees of freedom is in turn described by a diffusion equation.
The main attention is payed to Wilson loops, both on the lattice and in the continuum, which play a central role in mod- ern formulations of gauge theories and to the method of the 1/Nexpansion. Figure 1: A cusped Wilson loop (a) in N = 4 SYM on R4 (and by analytic continu-ation also on R3,1) is related to a pair of antiparallel lines (b) on S3 ×R. Lectures on Quantum Gravity and Black Holes Thomas Hartman Cornell University Please email corrections and suggestions to: hartman@cornell.edu Abstract These are the lecture notes for a one-semester graduate course on black holes and quantum gravity. 0000000651 00000 n In gauge theory, a Wilson loop (named after Kenneth G. Wilson) is a gauge-invariant observable obtained from the holonomy of the gauge connection around a given loop.
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