Exactly solvable field theories of closed strings
Abstract
Field theories of closed strings are shown to be exactly solvable for a central charge of matter fields c=16/m(m+1),m=1,2, 3, .... The twopoint function _{χ}(λ,N), in which λ is the cosmological constant and N^{1} is the string coupling constant, obeys a scaling law _{χ}(λ,N=N^{(m+1/2)}C((λ_{c}λ)N^{m/(m+1/2)}) in the limit in which N^{1} goes to zero and λ goes to a critical value λ_{c} we have determined the universal nonlinear differential equation satisfied by the function C. From this equation it is found that a phase transition takes place for some finite value of the scaling parameter (λ_{c}λ)N^{m/(m+1/2}); this transition is a ``condensation of handles'' on the world sheet, characterized by a divergence of the averaged genus of the world sheets. The cases m=2,3 are elaborated in more details, and the case m=1, which corresponds to the embedding of a bosonic string in 2 dimensions, is reduced to explicit quadratures.
Permanent address: Cybernetics Council and Academy of Sciences, ul. Vavilova 40, SU117 333 Moscow, USSR.
 Publication:

Physics Letters B
 Pub Date:
 February 1990
 DOI:
 10.1016/03702693(90)90818Q
 Bibcode:
 1990PhLB..236..144B