Lectures on topological quantum field theory

Labastida, J.M.F.; Lozano, Carlos

doi:10.1063/1.54705

Cited by 30 publications

(27 citation statements)

References 79 publications

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“…If the action of the model is trivial in cohomology the correlation functions of subsector operators do not depend on the coupling constants of the theory. Such correlators can then be calculated in the (classical) limit, as described for example in [19].…”

Section: Jhep05(2010)047mentioning

confidence: 99%

Cohomological reduction of sigma models

Candu

Creutzig

Mitev

et al. 2010

J. High Energ. Phys.

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This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme, we present a number of interesting examples, including symmetric superspaces G/G Z 2 and coset superspaces of the form G/G Z 4 .

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Section: Jhep05(2010)047mentioning

confidence: 99%

Cohomological reduction of sigma models

Candu

Creutzig

Mitev

et al. 2010

J. High Energ. Phys.

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“…One way is to develop a theory of infinite-dimensional calculus (BRST calculus). 10 The above discussion also gives an example of weak-strong duality, i.e. one theory of strong coupling is equivalent to a theory of weak coupling.…”

Section: Donaldson Witten and Seiberg Witten Invariantsmentioning

confidence: 97%

Qft, Strings and Low-Dimensional Topology

2002

Mod. Phys. Lett. A

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In between the 80's and 90's we witnessed deep interactions between mathematics and theoretical physics, especially in the understanding of low-dimensional topology in terms of quantum field theory. For example, Jones polynomials (Chern-Simons-Witten theory), Donaldson and Seiberg-Witten invariants (SUSY Yang-Mills theory) and mirror symmetry (T duality in strings) are all naturally understood in terms of QFT and strings. Recent developments indicate a close relationship between gauge theory and gravity theory both in physics and in low-dimensional topology. We shall survey these developments and report some of our work. We shall also find that the keys to connect geometric and physical objects are through symmetry and quantization.

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“…Since CS theory is a topological quantum field theory (TQFT) of Schwarz type, its action, equations of motion and observables do not require the existence of a metric. It is thus diffeomorphism invariant [22,24], i.e. invariant with respect to Diff 0 ðMÞ.…”

Section: A Symmetries Of Chern-simons Theorymentioning

confidence: 99%

Anyonic statistics and large horizon diffeomorphisms for loop quantum gravity black holes

Pithis

Euler

2015

Phys. Rev. D

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We investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of loop quantum gravity (LQG) black holes by means of their relation to the braid group. To this aim the symmetries of Chern-Simons theory are recapitulated with particular regard to the aforementioned type of diffeomorphisms. For the punctured spherical horizon, these are elements of the mapping class group of S 2 , which is almost isomorphic to a corresponding braid group on this particular manifold. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SUð2Þ k -Chern-Simons theory exhibits non-Abelian anyonic statistics. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-Abelian anyons play a significant role.

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Lectures on topological quantum field theory

Cited by 30 publications

References 79 publications

Cohomological reduction of sigma models

Cohomological reduction of sigma models

Qft, Strings and Low-Dimensional Topology

Anyonic statistics and large horizon diffeomorphisms for loop quantum gravity black holes

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