Open AccessTowards an explicit expression of the Seiberg-Witten map at all orders
Author(s) -
Stéphane Fidanza
Publication year - 2002
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2002/06/016
Subject(s) - noncommutative geometry , abelian group , supersymmetric gauge theory , gauge theory , gauge (firearms) , commutative property , order (exchange) , mathematics , hamiltonian lattice gauge theory , mathematical physics , gauge anomaly , pure mathematics , transformation (genetics) , introduction to gauge theory , quantum gauge theory , physics , theoretical physics , gauge fixing , gauge boson , archaeology , finance , economics , history , biochemistry , chemistry , gene
The Seiberg-Witten map links noncommutative gauge theories to ordinary gaugetheories, and allows to express the noncommutative variables in terms of thecommutative ones. Its explicit form can be found order by order in thenoncommutative parameter theta and the gauge potential A by the requirementthat gauge orbits are mapped on gauge orbits. This of course leavesambiguities, corresponding to gauge transformations, and there is an infinityof solutions. Is there one better, clearer than the others ? In the abeliancase, we were able to find a solution, linked by a gauge transformation toalready known formulas, which has the property of admitting a recursiveformulation, uncovering some pattern in the map. In the special case of a puregauge, both abelian and non-abelian, these expressions can be summed up, andthe transformation is expressed using the parametrisation in terms of the gaugegroup.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom