Nicolai maps for super Yang–Mills on the light cone

authored by

Olaf Lechtenfeld

Abstract

We construct Nicolai maps for supersymmetric Yang–Mills theory in four and ten spacetime dimensions in the light-cone gauge, where the elimination of non-propagating degrees of freedom causes nonlocal and four-fermi interactions in the Lagrangian. The presence of the latter used to be an obstruction to the Nicolai map, which has recently been overcome at the price of quantum corrections to the map. No gauge-fixing or ghost terms arise in this formulation, since only physical transverse degrees of freedom occur. We present an explicit form of the Nicolai map to second order in the gauge coupling. In four dimensions, a ‘chiral’ choice of the map leaves one of the two transverse gauge-field modes invariant, which forces the classical part of the map (on the other mode) to become a polynomial (quadratic in the gauge coupling, cubic in the gauge field)! In the power series expansion for the ten-dimensional map however, cancellations at each order in the coupling are systematic but incomplete, still leaving an infinite power series for the Nicolai map (on all eight transverse modes). Nevertheless, the existence of a polynomial variant is conceivable, also for the maximal N=4 theory in four dimensions.

Organisation(s)

Riemann Center for Geometry and Physics

Type

Artikel

Journal

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volume

856

No. of pages

7

ISSN

0370-2693

Publication date

09.2024

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.48550/arXiv.2406.04406 (Access: Offen)
https://doi.org/10.1016/j.physletb.2024.138950 (Access: Offen)