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University of Miami

1. Murgan, Rajan. Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain.

Degree: PhD, Physics (Arts and Sciences), 2008, University of Miami

URL: https://scholarlyrepository.miami.edu/oa_dissertations/69

The open spin-1/2 XXZ quantum spin chain with general integrable boundary terms is a fundamental integrable model. Finding a Bethe Ansatz solution for this model has been a subject of intensive research for many years. Such solutions for other simpler spin chain models have been shown to be essential for calculating various physical quantities, e.g., spectrum, scattering amplitudes, finite size corrections, anomalous dimensions of certain field operators in gauge field theories, etc. The first part of this dissertation focuses on Bethe Ansatz solutions for open spin chains with nondiagonal boundary terms. We present such solutions for some special cases where the Hamiltonians contain two free boundary parameters. The functional relation approach is utilized to solve the models at roots of unity, i.e., for bulk anisotropy values eta = i pi/(p+1) where p is a positive integer. This approach is then used to solve open spin chain with the most general integrable boundary terms with six boundary parameters, also at roots of unity, with no constraint among the boundary parameters. The second part of the dissertation is entirely on applications of the newly obtained Bethe Ansatz solutions. We first analyze the ground state and compute the boundary energy (order 1 correction) for all the cases mentioned above. We extend the analysis to study certain excited states for the two-parameter case. We investigate low-lying excited states with one hole and compute the corresponding Casimir energy (order 1/N correction) and conformal dimensions for these states. These results are later generalized to many-hole states. Finally, we compute the boundary S-matrix for one-hole excitations and show that the scattering amplitudes found correspond to the well known results of Ghoshal and Zamolodchikov for the boundary sine-Gordon model provided certain identifications between the lattice parameters (from the spin chain Hamiltonian) and infrared (IR) parameters (from the boundary sine-Gordon S-matrix) are made.
*Advisors/Committee Members: Rafael I. Nepomechie, James Nearing, Orlando Alvarez, Changrim Ahn.*

Subjects/Keywords: Integrable Models; Bethe Ansatz; Quantum Spin Chain

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Murgan, R. (2008). Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain. (Doctoral Dissertation). University of Miami. Retrieved from https://scholarlyrepository.miami.edu/oa_dissertations/69

Chicago Manual of Style (16^{th} Edition):

Murgan, Rajan. “Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain.” 2008. Doctoral Dissertation, University of Miami. Accessed August 08, 2020. https://scholarlyrepository.miami.edu/oa_dissertations/69.

MLA Handbook (7^{th} Edition):

Murgan, Rajan. “Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain.” 2008. Web. 08 Aug 2020.

Vancouver:

Murgan R. Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain. [Internet] [Doctoral dissertation]. University of Miami; 2008. [cited 2020 Aug 08]. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/69.

Council of Science Editors:

Murgan R. Bethe Ansatz and Open Spin-1/2 XXZ Quantum Spin Chain. [Doctoral Dissertation]. University of Miami; 2008. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/69

University of Miami

2. Ruszczycki, Blazej. Target Space Duality with Dilaton and Tachyon Field.

Degree: PhD, Physics (Arts and Sciences), 2007, University of Miami

URL: https://scholarlyrepository.miami.edu/oa_dissertations/17

We study the target space duality of classical two dimensional sigma models. The models with dilaton and tachyon field are analyzed. As a motivating example the historical electric-magnetic duality is presented. We review the construction of the duality transformation and the integrability conditions for the nonlinear sigma models with target spaces described by general metrics and antisymmetric two-forms. We generalize the formalism for the models whose actions contain the dilaton and tachyon field. For the dilaton field case it is required that the duality is a property solely of the target manifolds, independent of the world-sheet geometry. For both cases the duality transformation is established and the integrability conditions are calculated. The set of restrictions on geometrical data describing the models is obtained, the previously calculated condition on connections on target spaces is maintained in both cases.
*Advisors/Committee Members: Orlando Alvarez, James Nearing, Rafael Nepomechie, Gregory Galloway.*

Subjects/Keywords: String Theory; Duality

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Ruszczycki, B. (2007). Target Space Duality with Dilaton and Tachyon Field. (Doctoral Dissertation). University of Miami. Retrieved from https://scholarlyrepository.miami.edu/oa_dissertations/17

Chicago Manual of Style (16^{th} Edition):

Ruszczycki, Blazej. “Target Space Duality with Dilaton and Tachyon Field.” 2007. Doctoral Dissertation, University of Miami. Accessed August 08, 2020. https://scholarlyrepository.miami.edu/oa_dissertations/17.

MLA Handbook (7^{th} Edition):

Ruszczycki, Blazej. “Target Space Duality with Dilaton and Tachyon Field.” 2007. Web. 08 Aug 2020.

Vancouver:

Ruszczycki B. Target Space Duality with Dilaton and Tachyon Field. [Internet] [Doctoral dissertation]. University of Miami; 2007. [cited 2020 Aug 08]. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/17.

Council of Science Editors:

Ruszczycki B. Target Space Duality with Dilaton and Tachyon Field. [Doctoral Dissertation]. University of Miami; 2007. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/17

University of Miami

3. Sarisaman, Mustafa. Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces.

Degree: PhD, Physics (Arts and Sciences), 2010, University of Miami

URL: https://scholarlyrepository.miami.edu/oa_dissertations/357

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces. We first consider the case where sigma models based on real compact connected Lie groups of the same dimensionality and give examples using three dimensional models on target spaces. We show explicit construction of nonlocal conserved currents on the pseudodual manifold. We then switch the Lie group valued pseudoduality equations to Lie algebra valued ones, which leads to an infinite number of pseudoduality equations. We obtain an infinite number of conserved currents on the tangent bundle of the pseudodual manifold. Since pseudoduality imposes the condition that sigma models pseudodual to each other are based on symmetric spaces with opposite curvatures (i.e. dual symmetric spaces), we investigate pseudoduality transformation on the symmetric space sigma models in the third chapter. We see that there can be mixing of decomposed spaces with each other, which leads to mixings of the following expressions. We obtain the pseudodual conserved currents which are viewed as the orthonormal frame on the pullback bundle of the tangent space of G tilde which is the Lie group on which the pseudodual model based. Hence we obtain the mixing forms of curvature relations and one loop renormalization group beta function by means of these currents. In chapter four, we generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and by orthonormal coframe method on manifold SO(M). The component method produces the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where riemann normal coordinates valid on the second manifold. Torsion of the sigma model on M must vanish while it is nonvanishing on M tilde, and curvatures of the manifolds must be constant and the same because of anticommuting grassmann numbers. We obtain the similar results with the classical case in orthonormal coframe method. In case of super WZW sigma models pseudoduality equations result in three different pseudoduality conditions; flat space, chiral and antichiral pseudoduality. Finally we study the pseudoduality tansformations on symmetric spaces using two different methods again. These two methods yield similar results to the classical cases with the exception that commuting bracket relations in classical case turns out to be anticommuting ones because of the appearance of grassmann numbers. It is understood that constraint relations in case of non-mixing pseudoduality are the remnants of mixing pseudoduality. Once mixing terms are included in the pseudoduality the constraint relations disappear.
*Advisors/Committee Members: Orlando Alvarez, Rafael Nepomechie, James Nearing, Gregory Galloway.*

Subjects/Keywords: Pseudoduality; Sigma Model; WZW Model; String Theory

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sarisaman, M. (2010). Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces. (Doctoral Dissertation). University of Miami. Retrieved from https://scholarlyrepository.miami.edu/oa_dissertations/357

Chicago Manual of Style (16^{th} Edition):

Sarisaman, Mustafa. “Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces.” 2010. Doctoral Dissertation, University of Miami. Accessed August 08, 2020. https://scholarlyrepository.miami.edu/oa_dissertations/357.

MLA Handbook (7^{th} Edition):

Sarisaman, Mustafa. “Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces.” 2010. Web. 08 Aug 2020.

Vancouver:

Sarisaman M. Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces. [Internet] [Doctoral dissertation]. University of Miami; 2010. [cited 2020 Aug 08]. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/357.

Council of Science Editors:

Sarisaman M. Target Space Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces. [Doctoral Dissertation]. University of Miami; 2010. Available from: https://scholarlyrepository.miami.edu/oa_dissertations/357