Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-01-02
Phys.Rev. D47 (1993) 3430-3436
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, 5 eps figures contained in a uuencoded file, UVA-HET-92-10
Scientific paper
10.1103/PhysRevD.47.3430
Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small handles mapped into the target space. The sum is modded out by all diffeomorphisms on the world-sheet. This leaves a sum over disconnected classes of maps. We prove that the free energy gives a consistent result for all smooth maps of the torus into the torus which cover the target space $p$ times, where $p$ is prime, and conjecture that this is true for all coverings. Each class can also contain integrations over the positions of branch points and small handles which act as ``moduli'' on the surface. We show that the free energy is consistent for any number of handles and that the first few leading terms are consistent with contributions from maps with branch points.
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