Orientifolds and the Refined Topological String

Abstract

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which computes refined open string amplitudes for branes wrapping Seifert three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new invariants of torus knots that generalize the Kauffman polynomials. At large N, the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined topological strings on an orientifold of the resolved conifold, generalizing the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define and solve refined Chern-Simons theory for all ADE gauge groups.

References in corpus (15)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• R-Twisting and 4d/2d Correspondences
• Wall-Crossing in Coupled 2d-4d Systems
• Knot Homology from Refined Chern-Simons Theory
• Extended Holomorphic Anomaly in Gauge Theory
• Braids, Walls, and Mirrors
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Cohomological localization of Chern-Simons theory
• M-theory and a Topological String Duality
• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Non-Perturbative Topological Strings And Conformal Blocks
• Notes on supersymmetric Sp(N) theories with an antisymmetric tensor
• The Real Topological String on a local Calabi-Yau
• Composite Representation Invariants and Unoriented Topological String Amplitudes
• Composite Invariants and Unoriented Topological String Amplitudes

Cited by in corpus (19)

• The Superconformal Index of Class S Theories of Type D
• Refined Chern-Simons Theory and Topological String
• Gauge/Liouville Triality
• Colored Kauffman Homology and Super-A-polynomials
• Refined Chern-Simons versus Vogel universality
• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• $q$-Virasoro modular double and 3d partition functions
• Refined Black Hole Ensembles and Topological Strings
• The refined BPS index from stable pair invariants
• Refined large N duality for knots
• ABCD of Beta Ensembles and Topological Strings
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• M-theory interpretation of the real topological string
• Exact Chern-Simons / Topological String duality
• Two-fold refinement of non simply laced Chern-Simons theories
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
• Towards a gauge theory interpretation of the real topological string
• On refined Chern-Simons / topological string duality for classical gauge groups
• On partition functions of refined Chern-Simons theories on $S^3$