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Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid Vacua a
Author(s) -
SCHIMMRIGK ROLF
Publication year - 1993
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1993.tb43924.x
Subject(s) - cohomology , pure mathematics , holomorphic function , dilaton , compactification (mathematics) , string theory , physics , mathematics , torsion (gastropod) , string (physics) , antisymmetric relation , manifold (fluid mechanics) , rank (graph theory) , theoretical physics , group (periodic table) , mathematical physics , quantum mechanics , combinatorics , mechanical engineering , surgery , engineering , medicine
The role in string theory of manifolds of complex dimension $D_{crit} +2(Q-1)$ and positive first Chern class is described. In order to be useful forstring theory, the first Chern class of these spaces has to satisfy a certainrelation. Because of this condition the cohomology groups of such manifoldsshow a specific structure. A group that is particularly important is describedby $(D_{crit} + Q-1, Q-1)$--forms because it is this group which contains thehigher dimensional counterpart of the holomorphic $(D_{crit}, 0)$--form thatfigures so prominently in Calabi--Yau manifolds. It is shown that the higherdimensional manifolds do not, in general, have a unique counterpart of thisholomorphic form of rank $D_{crit}$. It is also shown that these manifoldslead, in general, to a number of additional modes beyond the standardCalabi--Yau spectrum. This suggests that not only the dilaton but also theother massless string modes, such as the antisymmetric torsion field, might berelevant for a possible stringy interpretation.Comment: 7 pages, NSF-ITP-93-3