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MiS Preprint

On Critical Dimensions of String Theories

Dimitry A. Leites and Christoph Sachse


Exactly 10 of all simple Lie superalgebras of vector fields on $1|N$-dimensional supercircles (superstrings) preserving a structure (either nothing, or a volume element, or a contact form) have nontrivial central extensions. The values of the central charges in (projective) spinor-oscillator representations of these stringy superalgebras associated with the adjoint module can be interpreted as critical dimensions of respective superstrings.

Apart from the well-known values 26, 10, 2 and 0 corresponding to $N=0$, 1, 2 and $>2$, respectively, for the contact type stringy superalgebras (Neveu--Schwarz and Ramond types alike), there are two more non-zero values of critical dimension: For the general and divergence-free algebras, both for $N=2$. These dimensions, found here, are $-1$ and $-2$, respectively. We also mention related problems.

Dec 23, 2006
Dec 23, 2006
MSC Codes:
stringy Lie superalgebra, critical dimension

Related publications

2007 Repository Open Access
D. A. Leites and Christoph Sachse

On critical dimensions of string theories

In: Mathematical physics : proceedings of the 12th Regional Conference ; Islamabad, Pakistan ; 27 March - 1 April 2006 / M. Jamil Aslam... (eds.)
New Jersey [u.a.] : World Scientific, 2007. - pp. 31-38