Supersymmetric surface operators, four-manifold theory and invariants in various dimensions

Abstract

We continue our program initiated in [1] to consider supersymmetric surface operators in a topologically twisted N = 2 pure SU (2) gauge theory, and apply them to the study of four-manifolds and related invariants.Elegant physical proofs of various seminal theorems in four-manifold theory obtained by Ozsváth and Szabó [2,3] and Taubes [4], will be furnished.In particular, we will show that Taubes' groundbreaking and difficult result -that the ordinary SW invariants are in fact the Gromov invariants which count pseudo-holomorphic curves embedded in a symplectic four-manifold X -nonetheless lends itself to a simple and concrete physical derivation in the presence of "ordinary" surface operators.As an offshoot, we will be led to several interesting and mathematically novel identities among the Gromov and "ramified" SW invariants of X, which in certain cases, also involve the instanton and monopole Floer homologies of its three-submanifold.Via these identities, and a physical formulation of the "ramified" Donaldson invariants of four-manifolds with boundaries, we will uncover completely new and economical ways of deriving and understanding various important

Locations

• Advances in Theoretical and Mathematical Physics - View - PDF
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF