scholarly journals Complementary projection defects and decomposition

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Renormalization Group Flows ◽  
Topological Quantum Field Theories

Abstract As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted $$ \mathcal{N} $$ N = (2, 2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.

GENERAL COVARIANCE, TOPOLOGICAL QUANTUM FIELD THEORIES AND FRACTIONAL STATISTICS

1992 ◽  
Vol 07 (02) ◽  
pp. 209-234 ◽  
Author(s):  
J. GAMBOA
Keyword(s):  
Hamiltonian Formalism ◽  
Field Theories ◽  
General Covariance ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Statistics ◽  
Multiply Connected ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Topological Quantum Field Theories

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. We study the relationship between both theories in 2 + 1 dimensions and we show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST–BFV quantization is reviewed in order to understand the topological approach proposed here.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND FROBENIUS ALGEBRAS

1996 ◽  
Vol 05 (05) ◽  
pp. 569-587 ◽  
Author(s):  
LOWELL ABRAMS
Keyword(s):  
Field Theories ◽  
Algebra Structure ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Direct Sums ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Simple Demonstration ◽  
Topological Quantum Field Theories

We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra structure with direct sums. We then classify the indecomposable Frobenius algebras as being either “annihilator algebras” — algebras whose socle is a principal ideal — or field extensions. The relationship between two-dimensional topological quantum field theories and Frobenius algebras is then formulated as an equivalence of categories. The proof hinges on our new characterization of Frobenius algebras. These results together provide a classification of the indecomposable two-dimensional topological quantum field theories.

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

EQUIVARIANT LOCALIZATION TECHNIQUES IN TOPOLOGICAL QUANTUM FIELD THEORIES

2010 ◽  
Vol 07 (02) ◽  
pp. 247-266
Author(s):  
ADRIAN VAJIAC
Keyword(s):  
Field Theories ◽  
Configuration Spaces ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Direct Study ◽  
Topological Quantum ◽  
Four Manifolds ◽  
Topological Quantum Field Theories

This paper proposes a different approach to derive Witten's formula relating Donaldson and Seiberg–Witten invariants for four-manifolds, via equivariant localization techniques. Our approach proposes a direct study on the Donaldson–Witten and Seiberg–Witten configuration spaces, not making use the theory of non-abelian monopoles.

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