DLCQ strings and branched covers of torii
Gordon W. Semenoff

TL;DR
This paper reviews how discrete light-cone quantization of strings constrains the Riemann surfaces in the path integral to branched covers of a torus, with implications for matrix string theory and explicit genus 1 checks.
Contribution
It establishes a connection between DLCQ string path integrals and branched covers of tori, providing explicit genus 1 verification and exploring links to matrix string theory.
Findings
Path integral of thermal string free energy constrained to branched covers of a torus.
Explicit genus 1 check supporting the theoretical constraint.
Potential relation between branched covers and matrix string model limits.
Abstract
In this lecture I will review some results about the discrete light-cone quantization (DLCQ) of strings and some connections of the results with matrix string theory. I will review arguments which show that, in the path integral representation of the thermal free energy of a string, the compactifications which are necessary to obtain discrete light-cone quantization constrains the integral over all Riemann surfaces of a given genus to the set of those Riemann surfaces which are branched covers of a particular torus. I then review an explicit check of this result at genus 1. I discuss the intriguing suggestion that these branched covers of a torus are related to those which are found in a certain limit of the matrix string model
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
