A Glimpse at the theory of Jordan - Banach triple systems

Sin resume

Superconformal current algebras and topological field theories

Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the $G/G$ coset theories. Their topological conformal algebra is generated by operators of dimensions $1$, $2$ and $3$ and can be regarded as an extension of the twisted $N=2$ superconformal algebra. These models possess an extended supersymmetry whose generators are exact in the topological BRST cohomology.Comment: 16 pages, phyzzx, US-FT-11/9

Pointwise Convergent Nets of Holomorphic Automorphisms of the Unit Bali of Cartan Factors

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Isometries and Automorphisms of the Spaces of Spinors

Sin resume

Summing over Spacetime Dimensions in Quantum Gravity

[EN] Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R-D are shown to be the result of summing over all dimensions D '>= D of R-D ', each summand taken in the absence of quantum gravityThe research of E.C. was funded by grant CU 338/1-1 from Deutsche Forschungsgemeinschaft (Germany). The research of J.M.I. was supported by grant no. RTI2018-102256-B-I00 (Spain). The authors acknowledge support from Vielberth Stiftung, Regensburg (GermanyCuriel, E.; Finster, F.; Isidro, J. (2020). Summing over Spacetime Dimensions in Quantum Gravity. Symmetry (Basel). 12(1):1-8. https://doi.org/10.3390/sym12010138S1812

On the WDVV Equation and M-Theory

A wide class of Seiberg-Witten models constructed by M-theory techniques and described by non-hyperelliptic Riemann surfaces are shown to possess an associative algebra of holomorphic differentials. This is a first step towards proving that also these models satisfy the Witten-Dijkgraaf-Verlinde-Verlinde equation. In this way, similar results known for simpler Seiberg-Witten models (described by hyperelliptic Riemann surfaces and constructed without recourse to M-theory) are extended to certain non-hyperelliptic cases constructed in M-theory. Our analysis reveals a connection between the algebra of holomorphic differentials on the Riemann surface and the configuration of M-theory branes of the corresponding Seiberg-Witten model.Comment: 30 pages, Latex, some corrections made, refs adde

Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

We formulate a conjecture about the structure of `upper lines' in the expansion of the colored Jones polynomial of a knot in powers of (q-1). The Melvin-Morton conjecture states that the bottom line in this expansion is equal to the inverse Alexander polynomial of the knot. We conjecture that the upper lines are rational functions whose denominators are powers of the Alexander polynomial. We prove this conjecture for torus knots and give experimental evidence that it is also true for other types of knots.Comment: 21 pages, 1 figure, LaTe

Coset Constructions in Chern-Simons Gauge Theory

Coset constructions in the framework of Chern-Simons topological gauge theories are studied. Two examples are considered: models of the types ${U(1)_p\times U(1)_q\over U(1)_{p+q}}\cong U(1)_{pq(p+q)}$ with $p$ and $q$ coprime integers, and ${SU(2)_m\times SU(2)_1\over SU(2)_{m+1}}$. In the latter case it is shown that the Chern-Simons wave functionals can be identified with t he characters of the minimal unitary models, and an explicit representation of the knot (Verlinde) operators acting on the space of $c<1$ characters is obtained.Comment: 15 page

Hyperbolic space in the Newtonian limit: The cosmological constant

[EN] In this paper, the cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.This research was supported by Grant No. RTI2018-102256-B-I00 (Spain).Castro-Palacio, JC.; Fernández De Córdoba, P.; Gallego Torromé, R.; Isidro, J. (2022). Hyperbolic space in the Newtonian limit: The cosmological constant. International Journal of Modern Physics D. 31(09):2250072-1-2250072-11. https://doi.org/10.1142/S02182718225007292250072-12250072-11310