Related papers: From quantum curves to topological string partitio…
The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Gamma, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators…
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We consider M-theory compactification on Calabi-Yau threefolds. The recently discovered connection between the BPS states of wrapped M2 branes and the topological string amplitudes on the threefold is used both as a tool to compute…
A connection between the conifold locus of the type II string on the $W\:P_{11226}^4$ Calabi-Yau manifold and the geometry of the quantum moduli of $N = 2$ $SU(2)$ super Yang-Mills is presented. This relation is obtained from the anomalous…
The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been…
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly…
Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric…
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo…
We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry $[0,1]\times\Sigma$, where $\Sigma$ is a generic…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
We present a string theoretic approach to surface counting in local Calabi--Yau fourfolds via supersymmetric localization in topologically twisted four-dimensional gauge theories. This approach is based on a spectral correspondence between…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
We examine the phase structure and the critical processes of the spectral curves that arise in the study of large N dualities between supersymmetric Yang-Mills theories and string models on local Calabi-Yau manifolds. These spectral curves…
The moduli spaces of Calabi--Yau (CY) manifolds are the special K\"ahler manifolds. The special K\"ahler geometry determines the low-energy effective theory which arises in Superstring theory after the compactification on a CY manifold. For…
We investigate the physics of the E-string theory and its compactifications as well as their applications to four-dimensional topology. In particular, we compute the partition function of the topologically twisted theory on $M_4\times T^2$,…
Aganagic, Dijkgraaf, Klemm, Mari\~{n}o and Vafa \cite{adkmv} predicted that the open string partition function on a smooth toric Calabi--Yau threefold should be a tau-function of multi-component KP hierarchy after considering the…
We present a string theory that reproduces the large-$N$ expansion of two dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli…