Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/142807
Title: SIGMA MODELS IN STRING AND M-THEORY
Authors: MEER ASHWINKUMAR MUHYIDIN BIN MEER AHMAD
ORCID iD:   orcid.org/0000-0002-4832-3277
Keywords: String theory, M-theory, Sigma models, D-branes, Mirror symmetry, M5-branes
Issue Date: 26-Jan-2018
Citation: MEER ASHWINKUMAR MUHYIDIN BIN MEER AHMAD (2018-01-26). SIGMA MODELS IN STRING AND M-THEORY. ScholarBank@NUS Repository.
Abstract: In this thesis, we explore the topic of applying sigma models to understand aspects of string theory and M-theory. Firstly, we describe supersymmetric A-branes and B-branes in open N = (2,2) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. This leads us to an equivariant version of the mathematical duality known as homological mirror symmetry. We then study correlation functions in the topological A-twisted version of the GNLSM, and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically BRST quantize the mirror theory to analyze this phenomenon. Secondly, we study the ground states and left-excited states of the A_{k-1} N = (2,0) little string theory. Via a theorem by Atiyah, these sectors can be captured by a supersymmetric nonlinear sigma model on CP^1 with target space the based loop group of SU(k). The ground states, described by L^2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. This provides us with a derivation and generalization of a mathematical duality conjectured by Braverman and Finkelberg. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
URI: http://scholarbank.nus.edu.sg/handle/10635/142807
Appears in Collections:Ph.D Theses (Open)

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