Surface holonomy and gauge 2-group. (English) Zbl 1081.53045

Lahiri, Amitabha

Int. J. Geom. Methods Mod. Phys. 1, No. 4, 299-309 (2004).

The author sketches his ideas on parallel transport for “infinitesimal” curves (“strings”) using the concept of a Lie 2-group from category theory [see J. Baez and A. D. Lauda, Theory Appl. Categ. 12, 423–491 (2004; Zbl 1056.18002)]. A similar approach is used in [J. Baez, Higher Yang-Mills theory, hep-th/0206130]. Applications or theorems are to be found elsewhere.
No reference is made to the by now standard methods for generalizing the classical holonomy concept [like A. Gray, Math. Z. 123, 290–300 (1971; Zbl 0222.53043), A. Swann, Weakening holonomy, Marchiafava, S. (ed.) et al., Proceedings of the 2nd meeting on quaternionic structures in mathematics and physics, Roma, Italy, 1999. Rome: Dipartimento di Matematica “Guido Castelnuovo”, Università di Roma “La Sapienza”, 405–415, electronic only (2001; Zbl 1028.53051), etc.] and the possible ways of dealing with holonomy in string theory [i.e., I. Agricola and Th. Friedrich, Math. Ann. 328, 711–748 (2004; Zbl 1055.53031), M. Mackaay and R. Picken, Adv. Math. 170, 287–339 (2002; Zbl 1034.53051)].

Reviewer: Ilka Agricola (Berlin)

MSC:

53C29	Issues of holonomy in differential geometry
70S15	Yang-Mills and other gauge theories in mechanics of particles and systems
20J15	Category of groups

Keywords:

surface holonomy; Lie 2-group

Citations:

Zbl 1056.18002; Zbl 0222.53043; Zbl 1028.53051; Zbl 1055.53031; Zbl 1034.53051

References:

[1]	Teitelboim C., Phys. Lett 167 pp 63–
[2]	DOI: 10.1016/S0003-4916(03)00147-7 · Zbl 1056.70013
[3]	Alvarez O., Nucl. Phys. 529 pp 689– · Zbl 0953.37018