Topological Gauge Theories and Group Cohomology
نویسنده
چکیده
We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H(BG,Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H(BG,Z) to #(G,Z). We generalize this correspondence to topological "spin" theories, which are defined on three manifolds with spin structure, and are related to what might be called Z2 graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.
منابع مشابه
Gauge Transformations, Brst Cohomology and Wigner’s Little Group
We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetri...
متن کاملGauge Transformations, Brst Cohomology and Wigner’s Little Group
We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetri...
متن کاملLie algebra cohomology and group structure of gauge theories
We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator Q for the Lie algebra cohomology induced by BRST generator Q. We also po...
متن کاملFirst non-abelian cohomology of topological groups II
In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...
متن کاملClassifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders
Citation Wen, Xiao-Gang. " Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders. " Physical Review D 88, no. 4 (August 2013). Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made...
متن کامل