Functional Approach to the Critical Dimension in Veneziano's Model

Minami, Masatsugu

doi:10.1143/PTP.52.1031

Functional Approach to the Critical Dimension in Veneziano's Model

Masatsugu Minami
(
- Kyoto U., RIMS
)

Apr, 1974

26 pages

Published in:

Prog.Theor.Phys. 52 (1974) 1031

DOI:

10.1143/PTP.52.1031

Report number:

RIMS-156

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Abstract: (Oxford Journals)

We give an explicit derivation of the critical dimension of space-time associated with the Veneziano model starting from the path-integral expression based on a Dirichlet-type boundary-value problem. It is shown that our expression for four-leg amplitudes happens to reduce to the beta-function formula of Veneziano only when the effective number of transverse dimensions is 24. Up to the goal, the transformation properties are not self-evident since our representation has a batch of the theta functions in the integrand. Our next concern is therefore with a discussion how the Möbius invariance or the reciprocal invariance is connected with the critical dimensionality.

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