cicyt UNIZAR
Full-text links:

Download:

Current browse context:

hep-th

Change to browse by:

References & Citations

Bookmark

(what is this?)
CiteULike logo BibSonomy logo Mendeley logo del.icio.us logo Digg logo Reddit logo ScienceWISE logo

High Energy Physics - Theory

Title: Conformal amplitude hierarchy and the Poincare disk

Abstract: The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d $O(n)$ model is studied as a function of $n$. For a generic value of $n$, the 4-point function has infinitely many amplitudes, whose landscape can be very spiky as the higher amplitude changes its sign many times at the simple poles, which generalize the unique pole of the energy operator amplitude at $n=0$. In the stadard parameterization of $n$ by angle in unit of $\pi$, we find that the zeros and poles happen at the rational angles, forming a hierarchical tree structure inherent in the Poincar\'{e} disk. Some relation between the amplitude and the Farey path, a piecewise geodesic that visits these zeros and poles, is suggested. In this hierarchy, the symmetry of the congruence subgroup $\Gamma(2)$ of $SL(2,\mathbb{Z})$ naturally arises from the two clearly distinct even/odd classes of the rational angles, in which one respectively gets the truncated operator algebras and the logarithmic 4-point functions.
Comments: 13 pages, 2 figures. see this version; corrections made; references added
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
Journal reference: J. Phys.: Conf. Ser. 965 (2018) 012036
Cite as: arXiv:1803.06938 [hep-th]
  (or arXiv:1803.06938v1 [hep-th] for this version)

Submission history

From: Hirohiko Shimada [view email]
[v1] Fri, 16 Mar 2018 16:56:03 GMT (872kb,D)