Details
| Original language | English |
|---|---|
| Article number | 114 |
| Journal | Journal of high energy physics |
| Volume | 2022 |
| Issue number | 2 |
| Publication status | Published - 15 Feb 2022 |
Abstract
We reconsider the supermembrane in a Minkowski background and in the light-cone gauge as a one-dimensional gauge theory of area preserving diffeomorphisms (APDs). Keeping the membrane tension T as an independent parameter we show that T is proportional to the gauge coupling g of this gauge theory, such that the small (large) tension limit of the supermembrane corresponds to the weak (strong) coupling limit of the APD gauge theory and its SU(N) matrix model approximation. A perturbative linearization of the supersymmetric theory suitable for a quantum mechanical path-integral treatment can be achieved by formulating a Nicolai map for the matrix model, which we work out explicitly to O(g4). The corresponding formulæ remain well-defined in the limit N → ∞; this result relies on a cancellation of infinities not present for the bosonic membrane, indicating that the N → ∞ limit does not exist for the purely bosonic matrix model. Furthermore we show that the map has improved convergence properties in comparison with the usual perturbative expansions because its Jacobian admits an expansion in g with a non-zero radius of convergence. Possible implications for unsolved issues with the matrix model of M theory are also mentioned.
Keywords
- Field Theories in Higher Dimensions, M(atrix) Theories, Supersymmetric Gauge Theory
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of high energy physics, Vol. 2022, No. 2, 114, 15.02.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A perturbative expansion scheme for supermembrane and matrix theory
AU - Lechtenfeld, Olaf
AU - Nicolai, Hermann
PY - 2022/2/15
Y1 - 2022/2/15
N2 - We reconsider the supermembrane in a Minkowski background and in the light-cone gauge as a one-dimensional gauge theory of area preserving diffeomorphisms (APDs). Keeping the membrane tension T as an independent parameter we show that T is proportional to the gauge coupling g of this gauge theory, such that the small (large) tension limit of the supermembrane corresponds to the weak (strong) coupling limit of the APD gauge theory and its SU(N) matrix model approximation. A perturbative linearization of the supersymmetric theory suitable for a quantum mechanical path-integral treatment can be achieved by formulating a Nicolai map for the matrix model, which we work out explicitly to O(g4). The corresponding formulæ remain well-defined in the limit N → ∞; this result relies on a cancellation of infinities not present for the bosonic membrane, indicating that the N → ∞ limit does not exist for the purely bosonic matrix model. Furthermore we show that the map has improved convergence properties in comparison with the usual perturbative expansions because its Jacobian admits an expansion in g with a non-zero radius of convergence. Possible implications for unsolved issues with the matrix model of M theory are also mentioned.
AB - We reconsider the supermembrane in a Minkowski background and in the light-cone gauge as a one-dimensional gauge theory of area preserving diffeomorphisms (APDs). Keeping the membrane tension T as an independent parameter we show that T is proportional to the gauge coupling g of this gauge theory, such that the small (large) tension limit of the supermembrane corresponds to the weak (strong) coupling limit of the APD gauge theory and its SU(N) matrix model approximation. A perturbative linearization of the supersymmetric theory suitable for a quantum mechanical path-integral treatment can be achieved by formulating a Nicolai map for the matrix model, which we work out explicitly to O(g4). The corresponding formulæ remain well-defined in the limit N → ∞; this result relies on a cancellation of infinities not present for the bosonic membrane, indicating that the N → ∞ limit does not exist for the purely bosonic matrix model. Furthermore we show that the map has improved convergence properties in comparison with the usual perturbative expansions because its Jacobian admits an expansion in g with a non-zero radius of convergence. Possible implications for unsolved issues with the matrix model of M theory are also mentioned.
KW - Field Theories in Higher Dimensions
KW - M(atrix) Theories
KW - Supersymmetric Gauge Theory
UR - http://www.scopus.com/inward/record.url?scp=85125343204&partnerID=8YFLogxK
U2 - 10.1007/JHEP02(2022)114
DO - 10.1007/JHEP02(2022)114
M3 - Article
AN - SCOPUS:85125343204
VL - 2022
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1029-8479
IS - 2
M1 - 114
ER -