Citation
Yen, Tinju Tim (1991) Strings, twodimensional gravity, and matrix models. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:04112011114355027
Abstract
Twodimensional models of quantum gravity have been solved using matrix model techniques. Furthermore, these solutions have turned out to be encoded in integrable nonlinear PDEs belonging to the KdV hierarchy. This thesis presents a new KdV recursion relation, distinct from one found previously by Dijkgraaf and Witten, for a certain class of theories known as the twomatrix models. The two recursion relations together are used to relate arbitrary correlation functions containing a puncture operator P (at any genus) to the three basic correlators <PP>, <PQ>, and <QQ> by unique algebraic expressions. (Q is the dilaton operator.) The derivation requires assuming a certain scaling law, whose justification is discussed. Other KdV recursion relations, given by Virasoro or Walgebra constraints, are possible for multimatrix models when an infinite number of couplings are added. These constraints have been presented for A_ntype models by Fukuma et al. and Dijkgraaf et ai. We derive analogous Virasoro constraints for the multimatrix models associated with the other simplylaced Lie algebras D_(2n+1), E_6, E_7, and E_8. As a check, it is verified that the proposed constraints imply operator scaling dimensions identical to those found by Kostov. It is then demonstrated that these Virasoro constraints (or, more generally, W algebra constraints) can be used to derive expressions for correlation functions containing a nonprimary operator in terms of correlation functions that only contain primary operators. The second subject of this thesis concerns the underlying symmetries of string theory as probed by fixedangle scattering at very high energy. The asymptotic behavior depends sensitively on the choice of the string vacuum. Therefore, we examine the effect of modifying the vacuum on the behavior of highenergy scattering amplitudes. In particular, highenergy fixedangle elastic scattering of openstring tachyons is studied explicitly. Tadpole corrections to the treelevel formulas are included. The main conclusion of the analysis is that symmetry relations among amplitudes at high energy seem to be unaffected by modifications of the vacuum, even though the amplitudes themselves do change.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Physics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  6 May 1991 
Record Number:  CaltechTHESIS:04112011114355027 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:04112011114355027 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6292 
Collection:  CaltechTHESIS 
Deposited By:  Tony Diaz 
Deposited On:  13 Apr 2011 16:50 
Last Modified:  04 Mar 2014 20:19 
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