Topological string theory

About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.

Geometric quantization, Chern-Simons quantum mechanics and one-dimensional sigma models

Abstract: The classical theory of a topological model which is constructed by setting the kinetic term of a (one-dimensional) sigma model at the classical level equal to zero is examined. The constraints and the geometry of the phase space of the supersymmetric extensions of the topological theory are studied. The rigid symmetries of a (supersymmetric) sigma model and its corresponding topological theory are gauged. Finally, the author examines the quantum theory of the one-dimensional sigma model in the limit where its kinetic term is set equal to zero and compare it with the quantum theory of the corresponding topological model.

When QCD strings can break

Abstract: Most of the observed properties of the string breaking in lattice gauge models in presence of charged dynamical matter can be simply understood in terms of a topological property of the loop expansion in the underlying string description of confinement. Similar considerations apply also to the breaking of the adjoint string.

TQFT string operations in open-closed string topology

Abstract: To open-closed cobordism surfaces, open-closed string topology associates topological quantum field theory (TQFT) operations, namely string operations, which depend only on homeomorphism types of surfaces and which satisfy the sewing property. We show that most TQFT string operations vanish in open-closed string topology. We describe those open-closed cobordisms with vanishing string operations, and give a short list of open-closed cobordisms with possibly nontrivial string operations.

Blocks and Vortices in the 3d ADHM Quiver Gauge Theory

Abstract: We study the hemisphere partition function of a three-dimensional $\mathcal{N}=4$ supersymmetric $U(N)$ gauge theory with one adjoint and one fundamental hypermultiplet -- the ADHM quiver theory. In particular, we propose a distinguished set of UV boundary conditions which yield Verma modules of the quantised chiral rings of the Higgs and Coulomb branches. In line with a recent proposal by two of the authors in collaboration with M. Bullimore, we show explicitly that the hemisphere partition functions recover the characters of these modules in two limits, and realise blocks gluing exactly to the partition functions of the theory on closed three-manifolds. We study the geometry of the vortex moduli space and investigate the interpretation of the vortex partition functions as equivariant indices of quasimaps to the Hilbert scheme of points in $\mathbb{C}^2$. We also investigate half indices of the ADHM quiver gauge theory in the presence of a line operator and discuss their geometric interpretation. Along the way we find interesting relations between our hemisphere blocks and related quantities in topological string theory and equivariant quantum K-theory.

Complete Lagrangian formulation for N = 4 topological string

Abstract: We give a Lagrangian and display all local symmetries for the $N=4$ topological string of Berkovits, Vafa and Siegel, the latter previously known in the superconformal gauge. Leading to a small $N=4$ superconformal algebra and exhibiting the manifest Lorentz invariance the model is proposed to be a framework for restoring the Lorentz invariance in $N=2$ string scattering amplitudes.