TY - JOUR

T1 - Double-scaled field theory at c = 1

AU - Moore, Gregory

N1 - Funding Information:
As is evident from the many footnotes above, this work was heavily influenced by many remarks and insights of T. Banks, N. Seiberg and S. Shenker. We thank them for their generous help and interest, and for comments on the manuscript. We also thank A. Dabholkar, D. Kutasov, E. Martinec, K. Rabe, R. Shankar, M. Staudacher and A. Zamolodchikov for useful conversations. We thank the Rutgers Department of Physics for hospitality. This work was supported by DOE grants DE-ACO2-76ER03075 and DE-FGO5-90ER40559 and by a Presidential Young Investigator Award.

PY - 1992/1/20

Y1 - 1992/1/20

N2 - We investigate the double-scaled free fermion theory of the c = 1 matrix model. We compute correlation functions of the eigenvalue density field and compare with the predictions of a relativistic boson theory. The c = 1 theory behaves as a relativistic theory at long distances, but has softer behavior at short distances. The soft short-distance behavior is closely related to the breakdown of the topological expansion at high energies. We also compute macroscopic loop amplitudes at c = 1, finding an integral representation for n-loop amplitudes to all orders of perturbation theory. We evaluate the integrals explicitly for two, three, and four macroscopic loops. The small loop length asymptotic expansion then gives correlation functions of local operators in the theory. The two-macroscopic-loop formula gives information on the spectrum and wave functions in the theory. The three- and four-loop amplitudes give scattering amplitudes for tachyon operators to all orders of perturbation theory. Again, the topological expansion breaks down at high energies. We compare our amplitudes with predictions from the Liouville theory.

AB - We investigate the double-scaled free fermion theory of the c = 1 matrix model. We compute correlation functions of the eigenvalue density field and compare with the predictions of a relativistic boson theory. The c = 1 theory behaves as a relativistic theory at long distances, but has softer behavior at short distances. The soft short-distance behavior is closely related to the breakdown of the topological expansion at high energies. We also compute macroscopic loop amplitudes at c = 1, finding an integral representation for n-loop amplitudes to all orders of perturbation theory. We evaluate the integrals explicitly for two, three, and four macroscopic loops. The small loop length asymptotic expansion then gives correlation functions of local operators in the theory. The two-macroscopic-loop formula gives information on the spectrum and wave functions in the theory. The three- and four-loop amplitudes give scattering amplitudes for tachyon operators to all orders of perturbation theory. Again, the topological expansion breaks down at high energies. We compare our amplitudes with predictions from the Liouville theory.

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U2 - 10.1016/0550-3213(92)90214-V

DO - 10.1016/0550-3213(92)90214-V

M3 - Article

AN - SCOPUS:0000177912

SN - 0550-3213

VL - 368

SP - 557

EP - 590

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -