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Selected topics in string field theory and physics of D-branes
Vošmera, Jakub ; Schnabl, Martin (advisor) ; Erler, Theodore (referee) ; Sachs, Ivo (referee)
We discuss certain aspects of string field theory and its applications in exploring the land- scape of classical string theory vacua. We start by giving a brief overview of various tree-level string field theories, as well as of some relevant mathematical background. As a byproduct of our general discussion of observables, we present a new gauge-invariant quantity for the A∞ formulation of open superstring field theory. Putting particular emphasis on perturba- tive methods, we proceed to review in detail the construction of tree-level effective actions governing the dynamics of a certain subset of degrees of freedom. In light of recent devel- opments, we also discuss efficient methods for evaluating certain vertices of zero-momentum effective actions for open superstring and heterotic string field theories in the presence of a global N = 2 worldsheet superconformal symmetry. We show how to apply this perturbative approach to study dynamics of the D(−1)/D3 system (both with and without a B-field), while also discussing a number of more complicated Dp-brane configurations. At generic points in their moduli spaces, such bound states of Dp-branes clearly cannot be described in terms of simple Dirichlet or Neumann boundary conditions. The rest of this thesis is therefore devoted to developing analytic...
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Selected topics in string field theory and physics of D-branes
Vošmera, Jakub ; Schnabl, Martin (advisor) ; Erler, Theodore (referee) ; Sachs, Ivo (referee)
We discuss certain aspects of string field theory and its applications in exploring the land- scape of classical string theory vacua. We start by giving a brief overview of various tree-level string field theories, as well as of some relevant mathematical background. As a byproduct of our general discussion of observables, we present a new gauge-invariant quantity for the A∞ formulation of open superstring field theory. Putting particular emphasis on perturba- tive methods, we proceed to review in detail the construction of tree-level effective actions governing the dynamics of a certain subset of degrees of freedom. In light of recent devel- opments, we also discuss efficient methods for evaluating certain vertices of zero-momentum effective actions for open superstring and heterotic string field theories in the presence of a global N = 2 worldsheet superconformal symmetry. We show how to apply this perturbative approach to study dynamics of the D(−1)/D3 system (both with and without a B-field), while also discussing a number of more complicated Dp-brane configurations. At generic points in their moduli spaces, such bound states of Dp-branes clearly cannot be described in terms of simple Dirichlet or Neumann boundary conditions. The rest of this thesis is therefore devoted to developing analytic...
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Nocommutative structures in quantum field theory
Peksová, Lada ; Jurčo, Branislav (advisor) ; Sachs, Ivo (referee) ; Golovko, Roman (referee)
In this thesis, structures defined via modular operads and properads are generalized to their non-commutative analogs. We define the connected sum for modular operads. This way we are able to construct the graded commutative product on the algebra over Feynman transform of the modular operad. This forms a Batalin-Vilkovisky algebra with symmetry given by the modular operad. We transfer this structure to the cohomology via the Homological perturbation lemma. In particular, we consider these constructions for Quantum closed and Quantum open modular operad. As a parallel project we introduce associative analog of Frobenius properad, called Open Frobenius properad. We construct the cobar complex over it and in the spirit of Barannikov interpret algebras over cobar complex as homological differential operators. Furthermore we present the IBA∞-algebras as analog of well-known IBL∞-algebras. 1
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