Details
| Original language | English |
|---|---|
| Article number | 138950 |
| Number of pages | 7 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 856 |
| Early online date | 8 Aug 2024 |
| Publication status | Published - Sept 2024 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 856, 138950, 09.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nicolai maps for super Yang–Mills on the light cone
AU - Lechtenfeld, Olaf
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85200965080&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2406.04406
DO - 10.48550/arXiv.2406.04406
M3 - Article
AN - SCOPUS:85200965080
VL - 856
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
SN - 0370-2693
M1 - 138950
ER -