arXiv subjects

M. Alvarez

Publications and source records attributed to M. Alvarez.

58 records · Page 4Linked to original sources

arXiv1994

Numerical knot invariants of finite type from Chern-Simons perturbation theory

Chern-Simons gauge theory for compact semisimple groups is analyzed from a perturbation theory point of view. The general form of the perturbative series expansion of a Wilson line is presented in terms of the Casimir operators of the gauge group. From this expansion new numerical knot invariants are obtained. These knot invariants turn out to be of finite type (Vassiliev invariants), and to possess an integral representation. Using known results about Jones, HOMFLY, Kauffman and Akutsu-Wadati polynomial invariants these new knot invariants are computed up to type six for all prime knots up to six crossings. Our results suggest that these knot invariants can be normalized in such a way that they are integer-valued.

hep-th↗

arXiv1994

Topological Matter in Four Dimensions

Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four dimensions. The framework in which the construction is based is constituted by the superspace associated to these algebras. The models show new features of topological quantum field theories which could provide either a mechanism for topological symmetry breaking, or the analog of two-dimensional mirror symmetry in four dimensions.

hep-th↗

arXiv1993

Breaking of Topological Symmetry

The coupling of topological matter to topological Yang-Mills theory in four dimensions is considered and a model is presented. It is shown that, contrary to the two-dimensional case, this coupling leads to a breaking of the topological symmetry. This means that the vacuum expectation values of the observables of the theory loose their invariance under small deformations of the metric while the action of the model possesses all the symmetries corresponding to the case with no coupling.

hep-th↗

arXiv1991

Analysis of Observables in Chern-Simons Perturbation Theory

Chern-Simons Theory with gauge group $SU(N)$ is analyzed from a perturbation theory point of view. The vacuum expectation value of the unknot is computed up to order $g^6$ and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten.

hep-th↗