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MINIMAL STRING THEORIES AND INTEGRABLE HIERARCHIES
by
Ramakrishnan Iyer
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
August 2011
Copyright 2011 Ramakrishnan Iyer
Object Description
| Title | Minimal string theories and integrable hierarchies |
| Author | Iyer, Ramakrishnan |
| Author email | ramaiyer@usc.edu;ramakrishnaniye@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Physics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2010-10-26 |
| Date submitted | 2011-08-02 |
| Date approved | 2011-08-03 |
| Restricted until | 2011-08-03 |
| Date published | 2011-08-03 |
| Advisor (committee chair) | Johnson, Clifford V. |
| Advisor (committee member) |
Pilch, Krzysztof Haas, Stephan Dappen, Werner Bonahon, Francis |
| Abstract | Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher-dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. ❧ The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2, 2m - 1) conformal minimal model backgrounds and the type 0A string in (2, 4m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2, 4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. ❧ In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string–like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string–like special points arise and are connected. In some cases, the framework endows the theories with a non–perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context. ❧ We then present evidence that the conjectured type II theories have smooth nonperturbative solutions, connecting two perturbative asymptotic regimes, in a ’t Hooft limit. Our technique also demonstrates evidence for new minimal string theories that are not apparent in a perturbative analysis. |
| Keyword | string theory; conformal field theory; minimal models; integrable hierarchies; painleve equations; non-linear partial and ordinary differential equations; dispersive water waves; random matrix models; type 0 minimal string theories |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Iyer, Ramakrishnan |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-IyerRamakr-238.pdf |
Description
| Title | Page 1 |
| Full text | MINIMAL STRING THEORIES AND INTEGRABLE HIERARCHIES by Ramakrishnan Iyer A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) August 2011 Copyright 2011 Ramakrishnan Iyer |
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