scholarly journals TOPOLOGICAL FIELD THEORIES AND THE PERIOD INTEGRALS

1993 ◽  
Vol 08 (17) ◽  
pp. 1627-1637 ◽  
Author(s):  
TOHRU EGUCHI ◽  
YASUHIKO YAMADA ◽  
SUNG-KIL YANG

We discuss topological Landau-Ginzburg theories coupled to two-dimensional topological gravity. We point out that the basic recursion relations for correlation functions of the two-dimensional gravity have exactly the same form as the Gauss-Manin differential equations for the period integrals of superpotentials. Thus the one-point functions on the sphere of the Landau-Ginzburg theories are given exactly by the period integrals. We discuss various examples, A-D-E minimal models and the c=3 topological theories.

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.


1990 ◽  
Vol 05 (07) ◽  
pp. 1369-1381 ◽  
Author(s):  
ROBERT MYERS

We examine two methods of fixing the gauge symmetry in Witten’s topological Yang-Mills theory. We find that both procedures produce the same nontrivial correlation functions. Our results also apply to other topological field theories, such as topological gravity.


1991 ◽  
Vol 06 (14) ◽  
pp. 1261-1268 ◽  
Author(s):  
YUNHAI CAI ◽  
GEORGE SIOPSIS

We discuss minimal conformal field theories M(p,q) coupled to 2-dimensional gravity in the continuum. We find a transformation that enables us to relate all models with p=2 to each other. We identify the Fock space in each model and calculate correlation functions. We thus show that the k-th multi-critical matrix model corresponds to the non-unitary minimal model with q=2k−1.


2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.


1992 ◽  
Vol 07 (24) ◽  
pp. 2215-2222 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUJI SUGAWARA

We study the twisted version of the supersymmetric G/T = SU (n)/ U (1)⊗(n−1) gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological Field theory, that is, the topological matter system in the K. Li's theory of two-dimensional gravity for the case of n = 2, and its generalization for n ≥ 3.


2007 ◽  
Vol 22 (38) ◽  
pp. 2939-2946
Author(s):  
M. O. TAHIM ◽  
C. A. S. ALMEIDA

In the celebrated Plebanski formalism of topological gravity, the constraints connecting topological field theories and gravity are imposed in spacetimes with trivial topology. In the braneworld context there are two distinct regions of the spacetime, namely, the bulk and the braneworld volume. In this work we show how to construct topological classical gravity in a scenario containing one extra dimension and a δ-function like three-brane which naturally emerges from a spontaneously broken discrete symmetry. Starting from a D = 5 theory we obtain the action for General Relativity in the Palatini form in the bulk as well as in the braneworld volume. This result is important for future insights about quantum gravity on brane scenarios.


1993 ◽  
Vol 08 (24) ◽  
pp. 2277-2283 ◽  
Author(s):  
ROGER BROOKS

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of topological quantum field theories (TQFTs). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for (2+1)- and (1+1)-dimensional space-times foliated as M=Σ × ℝ, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.


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