Two Conjectures on Gauge Theories, Gravity, and Infinite Dimensional Kac-Moody Groups

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dc.creatorGanor, Ori J.
dc.date1999-03-12
dc.date1999-10-28
dc.date.accessioned2026-07-07T04:26:08Z
dc.date.available2026-07-07T04:26:08Z
dc.descriptionWe propose that the structure of gauge theories, the $(2,0)$ and little-string theories is encoded in a unique function on the real group manifold $E_{10}(R)$. The function is invariant under the maximal compact subgroup $K$ acting on the right and under the discrete U-duality subgroup $E_{10}(Z)$ on the left. The manifold $E_{10}(Z)\backslash E_{10}(R) /K$ contains an infinite number of periodic variables. The partition function of U(n), N=4 Super-Yang-Mills theory on $T^4$, with generic SO(6) R-symmetry twists, for example, is derived from the $n^{th}$ coefficient of the Fourier transform of the function with respect to appropriate periodic variables, setting other variables to the R-symmetry twists and the radii of $T^4$. In particular, the partition function of nonsupersymmetric Yang-Mills theory is a special case, obtained from the twisted $(2,0)$ or little-string theories. The function also seems to encode the answer to questions about M-theory on an arbitrary $T^8$. The second conjecture that we wish to propose is that this function is harmonic with respect to the $E_{10}(R)$ invariant metric. In a similar fashion, we propose that there exists a function on the infinite Kac-Moody group $DE_{18}$ that encodes the twisted partition functions of the $E_8$ 5+1D theories as well as answers to questions about the heterotic string on $T^7$.
dc.description54pp LaTeX, Added references, changed subsection (8.2)
dc.identifierhttps://arxiv.org/abs/hep-th/9903110
dc.identifierhttp://arxiv.org/abs/hep-th/9903110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/55988
dc.subjectHigh Energy Physics - Theory
dc.titleTwo Conjectures on Gauge Theories, Gravity, and Infinite Dimensional Kac-Moody Groups
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