129 citations · 1.2k across the 37 of their papers we have counts for
10 papers · 1 filter
Lectures on mathematical aspects of (twisted) supersymmetric gauge theories
Kevin Costello, Claudia Scheimbauer
Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a r…
Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
Kevin J. Costello, Si Li
Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Koda…
A geometric construction of the Witten genus, II
Kevin J. Costello
I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of thi…
Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4
Kevin J. Costello
These notes explore some aspects of formal derived geometry related to classical field theory. One goal is to explain how many important classical field theories in physics -- such…
A geometric construction of the Witten genus, I
Kevin J. Costello
I describe how the Witten genus of a complex manifold can be seen from a rigorous analysis of a certain two-dimensional quantum field theory of maps from a surface to .
Closed String TCFT for Hermitian Calabi-Yau Elliptic Spaces
Kevin J. Costello, Thomas Tradler, Mahmoud Zeinalian
We describe an explicit action of the prop of the chains on the moduli space of Riemann surfaces on the Hochschild complex of a Calabi-Yau elliptic space. One example of such an el…